The atom-bond sum-connectivity(ABS)index,put forward by[J.Math.Chem.,2022,60(10):20812093],exhibits a strong link with the acentric factor of octane isomers.The experimental physico-chemical properties of octane isome...The atom-bond sum-connectivity(ABS)index,put forward by[J.Math.Chem.,2022,60(10):20812093],exhibits a strong link with the acentric factor of octane isomers.The experimental physico-chemical properties of octane isomers,such as boiling point,of formation are found to be better measured by the ABS index than by the Randi,atom-bond connectivity(ABC),and sum-connectivity(SC)indices.One important source of information for researching the molecular structure is the bounds for its topological indices.The extrema of the ABS index of the line,total,and Mycielski graphs are calculated in this work.Moreover,the pertinent extremal graphs were illustrated.展开更多
A graph is Hamiltonian if it contains a cycle that visits each vertex of the graph exactly once.A chord of a cycle C is an edge that joins two non-consecutive vertices of C.A graph of order n is chorded pancyclic if i...A graph is Hamiltonian if it contains a cycle that visits each vertex of the graph exactly once.A chord of a cycle C is an edge that joins two non-consecutive vertices of C.A graph of order n is chorded pancyclic if it contains a chorded cycle of length k for every integer k with 4≤k≤n.In 2018,Ferro and Lesniak gave an edge number conditon for the Hamiltonicity(and the chorded pancyclicity)of balanced and unbalanced k-partite graphs.In this paper,we extend the main results of Ferro and Lesniak,and provide an edge condition for the Hamiltonicity(and the chorded pancyclicity)of balanced and unbalanced k-partite graphs with given minimum degree,respectively.展开更多
Let Un be the set of connected unicyclic graphs of order n and girth g.Let C(T_(1),T_(2),...,T_(g))Un be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in the anticlockwise direction)by identifying vi with the root of a...Let Un be the set of connected unicyclic graphs of order n and girth g.Let C(T_(1),T_(2),...,T_(g))Un be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in the anticlockwise direction)by identifying vi with the root of a rooted tree Ti of order ni for each i=1,2,...,g,where ni≥1 and∑^(g)_(i=1)n_(i)=n.Let S(n_(1),n_(2),...,n_(g))be obtained from C(T_(1),T_(2),..,T_(g))by replacing each Ti by a rooted star Sni with the center as its root.Let U(n_(1),n_(2),...,ng)be the set of unicyclic graphs which differ from the unicyclic graph S(n_(1),n_(2),...,n_(g))only up to a permutation of ni's.In this paper,the graph with the minimal least signless Laplacian eigenvalue(respectively,the graph with maximum signless Laplacian spread)in U(n_(1),n_(2),...,n_(g))is determined.展开更多
This article studies the consensus problem with directed graphs for general linear multi-agent systems.New distributed state-feedback protocols with dynamic event-triggered(DET)mechanisms are proposed for directed gra...This article studies the consensus problem with directed graphs for general linear multi-agent systems.New distributed state-feedback protocols with dynamic event-triggered(DET)mechanisms are proposed for directed graphs that are strongly connected and weight-balanced,general strongly connected,and have spanning trees,respectively.It is proven that strictly positive minimum inter-event times(MIETs)are ensured using the designed DET mechanisms.Several numerical examples are presented to illustrate the effectiveness of the theoretical results.Compared with existing results,our results have the following merits:1)DET mechanisms are designed to determine the sampling instants,which can reduce the communication frequency between agents compared with static mechanisms;2)We focus on the consensus problem on directed graphs,which is more general than existing related results on undirected graphs;3)The existence of positive MIETs is shown to be guaranteed by the designed DET sampling strategies while existing related results can only exclude Zeno behavior.展开更多
With network attack technology continuing to develop,traditional anomaly traffic detection methods that rely on feature engineering are increasingly insufficient in efficiency and accuracy.Graph Neural Network(GNN),a ...With network attack technology continuing to develop,traditional anomaly traffic detection methods that rely on feature engineering are increasingly insufficient in efficiency and accuracy.Graph Neural Network(GNN),a promising Deep Learning(DL)approach,has proven to be highly effective in identifying intricate patterns in graph⁃structured data and has already found wide applications in the field of network security.In this paper,we propose a hybrid Graph Convolutional Network(GCN)⁃GraphSAGE model for Anomaly Traffic Detection,namely HGS⁃ATD,which aims to improve the accuracy of anomaly traffic detection by leveraging edge feature learning to better capture the relationships between network entities.We validate the HGS⁃ATD model on four publicly available datasets,including NF⁃UNSW⁃NB15⁃v2.The experimental results show that the enhanced hybrid model is 5.71%to 10.25%higher than the baseline model in terms of accuracy,and the F1⁃score is 5.53%to 11.63%higher than the baseline model,proving that the model can effectively distinguish normal traffic from attack traffic and accurately classify various types of attacks.展开更多
This paper delves into effective pathways for transforming course ecosystems from resource provision to knowledge service and competency development through university-enterprise collaboration in co-building knowledge...This paper delves into effective pathways for transforming course ecosystems from resource provision to knowledge service and competency development through university-enterprise collaboration in co-building knowledge graphs and intelligent shared courses.This approach enables personalized,learning-driven teaching.Based on knowledge graphs and integrated teacher-machine-student smart teaching scenarios,it not only innovates autonomous learning environments and human-computer interaction models while optimizing teaching experiences for both instructors and students,but also effectively addresses the issues of students’“scattered,superficial,and fragmented learning”.This establishes the foundation for personalized teaching tailored to individual aptitudes.展开更多
An injective k-edge coloring of a graph G is k-edge coloringκof G such thatκ(e1)≠κ(e3)for any three consecutive edges ei,e2 and e3 of a path or a triangle.The injective chromatic index of G,denoted by x'i(G),i...An injective k-edge coloring of a graph G is k-edge coloringκof G such thatκ(e1)≠κ(e3)for any three consecutive edges ei,e2 and e3 of a path or a triangle.The injective chromatic index of G,denoted by x'i(G),is the smallest integer k such that G has an injective k-edge coloring.In this paper,we prove that x'i(G)≤9 if G is a planar graph with maximum degreeΔ≤4,girth g≥6 and without intersecting 6-cycles.展开更多
Structural variations(SVs≥50 bp)are a critical but underexplored source of genetic diversity in cattle,shaping traits vital for productivity,adaptability,and health.Advances in long-read sequencing,pangenome graph co...Structural variations(SVs≥50 bp)are a critical but underexplored source of genetic diversity in cattle,shaping traits vital for productivity,adaptability,and health.Advances in long-read sequencing,pangenome graph construction,and near-complete genome assemblies now allow accurate SV detection and genotyping.These innovations overcome the limitations of single-reference genomes,enabling the discovery of complex SVs,including nested and overlapping variants,and providing access to previously inaccessible genomic regions such as centromeres and telomeres.This review highlights the current landscape of cattle SV research,with emphasis on integrating longread sequencing and pangenome frameworks to uncover breed-specific and population-level variation.While many SVs are linked to economically important traits such as feed efficiency and disease resistance,their broader regulatory impacts remain an active area of investigation.Emerging functional genomics approaches,including transcriptomics,epigenomics,and genome editing,will clarify how SVs influence gene regulation and phenotype.Looking forward,the integration of SV catalogs with multi-omics data,imputation resources,and artificial intelligence-driven models will be essential for translating discoveries into breeding and conservation applications.Integrating structural variants into breeding pipelines promises to revolutionize livestock genomics,enabling precision selection and sustainable agriculture despite challenges in cost,data sharing,and functional validation.展开更多
Chain graphs are{2K_(2),C_(3),C_(5)}-free graphs.Balaban index and sum-Balaban index are two important topological indices.In this paper,we concentrate on the subclass of bicyclic connected chain graphs,identifying th...Chain graphs are{2K_(2),C_(3),C_(5)}-free graphs.Balaban index and sum-Balaban index are two important topological indices.In this paper,we concentrate on the subclass of bicyclic connected chain graphs,identifying the extremal graphs that exhibit the minimum or maximum Balaban index and sum-Balaban index within this class.Moreover,we provide a systematic ordering of all bicyclic connected chain graphs according to the magnitude of their Balaban index and sum-Balaban index.展开更多
Accurately predicting the synthesizability of inorganic crystal materials serves as a pivotal tool for the efficient screening of viable candidates,substantially reducing the costs associated with extensive experiment...Accurately predicting the synthesizability of inorganic crystal materials serves as a pivotal tool for the efficient screening of viable candidates,substantially reducing the costs associated with extensive experimental trial-and-error processes.However,existing methods,limited by static structural descriptors such as chemical composition and lattice parameters,fail to account for atomic vibrations,which may introduce spurious correlations and undermine predictive reliability.Here,we propose a deep learning model termed integrating graph and dynamical stability(IGDS)for predicting the synthesizability of inorganic crystals.IGDS employs graph representation learning to construct crystal graphs that precisely capture the static structures of crystals and integrates phonon spectral features extracted from pre-trained machine learning interatomic potentials to represent their dynamic properties.Our model exhibits outstanding performance in predicting the synthesizability of low-energy unsynthesizable crystals across 41 material systems,achieving precision and recall values of 0.916/0.863 for ternary compounds.By capturing both static structural descriptors and dynamic features,IGDS provides a physics-informed method for predicting the synthesizability of inorganic crystals.This approach bridges the gap between theoretical design concepts and their practical implementation,thereby streamlining the development cycle of new materials and enhancing overall research efficiency.展开更多
Knowledge graphs,which combine structured representation with semantic modeling,have shown great potential in knowledge expression,causal inference,and automated reasoning,and are widely used in fields such as intelli...Knowledge graphs,which combine structured representation with semantic modeling,have shown great potential in knowledge expression,causal inference,and automated reasoning,and are widely used in fields such as intelligent question answering,decision support,and fault diagnosis.As high-speed train systems become increasingly intelligent and interconnected,fault patterns have grown more complex and dynamic.Knowledge graphs offer a promising solution to support the structured management and real-time reasoning of fault knowledge,addressing key requirements such as interpretability,accuracy,and continuous evolution in intelligent diagnostic systems.However,conventional knowledge graph construction relies heavily on domain expertise and specialized tools,resulting in high entry barriers for non-experts and limiting their practical application in frontline maintenance scenarios.To address this limitation,this paper proposes a fault knowledge modeling approach for high-speed trains that integrates structured logic diagrams with knowledge graphs.The method employs a seven-layer logic structure—comprising fault name,applicable vehicles,diagnostic logic,signal parameters,verification conditions,fault causes,and emergency measures—to transform unstructured knowledge into a visual and hierarchical representation.A semantic mapping mechanism is then used to automatically convert logic diagrams into machine-interpretable knowledge graphs,enabling dynamic reasoning and knowledge reuse.Furthermore,the proposed method establishes a three-layer architecture—logic structuring,knowledge graph transformation,and dynamic inference—to bridge human-expert logic with machinebased reasoning.Experimental validation and system implementation demonstrate that this approach not only improves knowledge interpretability and inference precision but also significantly enhances modeling efficiency and system maintainability.It provides a scalable and adaptable solution for intelligent operation and maintenance platforms in the high-speed rail domain.展开更多
In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizh...In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizhong Zhou,Hongxia Liu and Yang Xu(2022).Then,an A_(α)-spectral condition is given to ensure that G is a fractional ID-[a,b]-factor-critical covered graph and an(a,b,k)-factor-critical graph,respectively.In fact,(a,b,k)-factor-critical graph is a graph which has an[a,b]-factor for k=0.Thus,these above results extend the results of Jia Wei and Shenggui Zhang(2023)and Ao Fan,Ruifang Liu and Guoyan Ao(2023)in some sense.展开更多
Let R be afinite commutative ring with identity 1.The U-clean graph of R,denoted by U-Cl(R),is a graph with vertices in form(e,u),where e is a nonzero idempotent of R and u is a unit of R.In this paper,some basic prope...Let R be afinite commutative ring with identity 1.The U-clean graph of R,denoted by U-Cl(R),is a graph with vertices in form(e,u),where e is a nonzero idempotent of R and u is a unit of R.In this paper,some basic properties of U-Cl(R)and the explicit structures of U-Cl(Zp×Zq)are given,where p,q are primes.We prove that U-Cl(Zp×Zq)is Eulerlian if and only if p=2,q=2.Moreover,the clique number,the chromatic number of the U-clean graph for some classes of rings are given in this paper.展开更多
A graph G is H-free,if it contains no H as a subgraph.A graph G is said to be H-minor free,if it does not contain H as a minor.In 2010,Nikiforov asked that what the maximum spectral radius of an H-free graph of order ...A graph G is H-free,if it contains no H as a subgraph.A graph G is said to be H-minor free,if it does not contain H as a minor.In 2010,Nikiforov asked that what the maximum spectral radius of an H-free graph of order n is.In this paper,we consider some Brualdi-Solheid-Turan type problems on bipartite graphs.In 2015,Zhai,Lin and Gong in[Linear Algebra Appl.,2015,471:21-27]proved that if G is a bipartite graph with order n≥2k+2 and ρ(G)≥ρ(K_(k,n-k)),then G contains a C_(2k+2) unless G≌K_(k,n-k).First,we give a new and more simple proof for the above theorem.Second,we prove that if G is a bipartite graph with order n≥2k+2 and ρ(G)≥ρ(K_(k,n-k)),then G contains all T_(2k+3) unless G≌K_(k,n-k).Finally,we prove that among all outerplanar bipartite graphs on n≥308026 vertices,K_(1,n-1) attains the maximum spectral radius.展开更多
The concept of matching energy was proposed by Gutman and Wagner firstly in 2012. Let G be a simple graph of order n and λ1, λ2, . . . , λn be the zeros of its matching polynomial. The matching energy of a graph G ...The concept of matching energy was proposed by Gutman and Wagner firstly in 2012. Let G be a simple graph of order n and λ1, λ2, . . . , λn be the zeros of its matching polynomial. The matching energy of a graph G is defined as ME(G) = Pni=1 |λi|. By the famous Coulson’s formula, matching energies can also be calculated by an improper integral depending on a parameter. A k-claw attaching graph Gu(k) refers to the graph obtained by attaching k pendent edges to the graph G at the vertex u, where u is called the root of Gu(k). In this paper, we use some theories of mathematical analysis to obtain a new technique to compare the matching energies of two k-claw attaching graphs Gu(k) and Hv(k) with the same order, that is, limk→∞[ME(Gu(k)) − ME(Hv(k))] = ME(G − u) − ME(H − v). By the technique, we finally determine unicyclic graphs of order n with the 9th to 13th minimal matching energies for all n ≥ 58.展开更多
A graph G is called d-degenerate if every subgraph of G has a vertex of degree at most d.It was known that planar graphs are 5-degenerate and every planar graph without k-cycles for some prescribed k∈{3,5,6}is 3-dege...A graph G is called d-degenerate if every subgraph of G has a vertex of degree at most d.It was known that planar graphs are 5-degenerate and every planar graph without k-cycles for some prescribed k∈{3,5,6}is 3-degenerate.In this paper,we show that if G is a planar graph without kites and 9-or 10-cycles,then G is 3-degenerate,hence 4-choosable and list vertex 2-arborable.展开更多
A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vert...A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vertex.This concept was introduced by Tutte as an extension of face colorings,and Tutte in 1954 conjectured that every bridgeless graph admits a nowhere-zero 5-flow,known as the 5-Flow Conjecture.This conjecture is verified for some graph classes and remains unresolved as of today.In this paper,we show that every bridgeless graph of Euler genus at most 20 admits a nowhere-zero 5-flow,which improves several known results.展开更多
Determining the crossing number of a given graph is NP-complete. The cycle of length m is denoted by Cm = v1v2…vmv1. G^((1))_(m) (m ≥ 5) is the graph obtained from Cm by adding two edges v1v3 and vlvl+2 (3 ≤ l ≤ m...Determining the crossing number of a given graph is NP-complete. The cycle of length m is denoted by Cm = v1v2…vmv1. G^((1))_(m) (m ≥ 5) is the graph obtained from Cm by adding two edges v1v3 and vlvl+2 (3 ≤ l ≤ m−2), G^((2))m (m ≥ 4) is the graph obtained from Cm by adding two edges v1v3 and v2v4. The famous Zarankiewicz’s conjecture on the crossing number of the complete bipartite graph Km,n states that cr(Km,n)=Z(m,n)=[m/2][m-1/2][n/2[n-1/2].Based on Zarankiewicz’s conjecture, a natural problem is to study the change in the crossingnumber of the graphs obtained from the complete bipartite graph by adding certain edge sets.If Zarankiewicz’s conjecture is true, this paper proves that cr(G^((1))_(m)+Kn)=Z(m,n)+2[n/2] and cr(G^((2))_(m)+Kn)=Z(m,n)+n.展开更多
DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improve...DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improves the results of[Discrete Math.,2018,341(7):1983–1986]and[Discrete Appl.Math.,2020,277:245–251].展开更多
For a graph G,a vertex is said to be pendant if its neighborhood contains exactly one vertex.In this paper,we determine the extremal graphs among all n-vertex graphs with the minimum spectral radius andβpendant verti...For a graph G,a vertex is said to be pendant if its neighborhood contains exactly one vertex.In this paper,we determine the extremal graphs among all n-vertex graphs with the minimum spectral radius andβpendant vertices,whereβe{1,2,3,4,n-3,n-2,n-1}.展开更多
基金Supported by Ningbo NSF(No.2021J234)Zhejiang Provincial Philosophy and Social Sciences Planning Project(No.24NDJC057YB)。
文摘The atom-bond sum-connectivity(ABS)index,put forward by[J.Math.Chem.,2022,60(10):20812093],exhibits a strong link with the acentric factor of octane isomers.The experimental physico-chemical properties of octane isomers,such as boiling point,of formation are found to be better measured by the ABS index than by the Randi,atom-bond connectivity(ABC),and sum-connectivity(SC)indices.One important source of information for researching the molecular structure is the bounds for its topological indices.The extrema of the ABS index of the line,total,and Mycielski graphs are calculated in this work.Moreover,the pertinent extremal graphs were illustrated.
文摘A graph is Hamiltonian if it contains a cycle that visits each vertex of the graph exactly once.A chord of a cycle C is an edge that joins two non-consecutive vertices of C.A graph of order n is chorded pancyclic if it contains a chorded cycle of length k for every integer k with 4≤k≤n.In 2018,Ferro and Lesniak gave an edge number conditon for the Hamiltonicity(and the chorded pancyclicity)of balanced and unbalanced k-partite graphs.In this paper,we extend the main results of Ferro and Lesniak,and provide an edge condition for the Hamiltonicity(and the chorded pancyclicity)of balanced and unbalanced k-partite graphs with given minimum degree,respectively.
基金This research is supported by NSFC(Nos.12171154,12301438)the Chenguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education Commission(No.23CGA37)。
文摘Let Un be the set of connected unicyclic graphs of order n and girth g.Let C(T_(1),T_(2),...,T_(g))Un be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in the anticlockwise direction)by identifying vi with the root of a rooted tree Ti of order ni for each i=1,2,...,g,where ni≥1 and∑^(g)_(i=1)n_(i)=n.Let S(n_(1),n_(2),...,n_(g))be obtained from C(T_(1),T_(2),..,T_(g))by replacing each Ti by a rooted star Sni with the center as its root.Let U(n_(1),n_(2),...,ng)be the set of unicyclic graphs which differ from the unicyclic graph S(n_(1),n_(2),...,n_(g))only up to a permutation of ni's.In this paper,the graph with the minimal least signless Laplacian eigenvalue(respectively,the graph with maximum signless Laplacian spread)in U(n_(1),n_(2),...,n_(g))is determined.
基金supported in part by the Natural Science Foundation of China(62273227,92367203)the Open Research Project of the State Key Laboratory of Industrial Control Technology,China(ICT2024B68)。
文摘This article studies the consensus problem with directed graphs for general linear multi-agent systems.New distributed state-feedback protocols with dynamic event-triggered(DET)mechanisms are proposed for directed graphs that are strongly connected and weight-balanced,general strongly connected,and have spanning trees,respectively.It is proven that strictly positive minimum inter-event times(MIETs)are ensured using the designed DET mechanisms.Several numerical examples are presented to illustrate the effectiveness of the theoretical results.Compared with existing results,our results have the following merits:1)DET mechanisms are designed to determine the sampling instants,which can reduce the communication frequency between agents compared with static mechanisms;2)We focus on the consensus problem on directed graphs,which is more general than existing related results on undirected graphs;3)The existence of positive MIETs is shown to be guaranteed by the designed DET sampling strategies while existing related results can only exclude Zeno behavior.
基金National Natural Science Foundation of China(Grant No.62103434)National Science Fund for Distinguished Young Scholars(Grant No.62176263).
文摘With network attack technology continuing to develop,traditional anomaly traffic detection methods that rely on feature engineering are increasingly insufficient in efficiency and accuracy.Graph Neural Network(GNN),a promising Deep Learning(DL)approach,has proven to be highly effective in identifying intricate patterns in graph⁃structured data and has already found wide applications in the field of network security.In this paper,we propose a hybrid Graph Convolutional Network(GCN)⁃GraphSAGE model for Anomaly Traffic Detection,namely HGS⁃ATD,which aims to improve the accuracy of anomaly traffic detection by leveraging edge feature learning to better capture the relationships between network entities.We validate the HGS⁃ATD model on four publicly available datasets,including NF⁃UNSW⁃NB15⁃v2.The experimental results show that the enhanced hybrid model is 5.71%to 10.25%higher than the baseline model in terms of accuracy,and the F1⁃score is 5.53%to 11.63%higher than the baseline model,proving that the model can effectively distinguish normal traffic from attack traffic and accurately classify various types of attacks.
基金supported by Harbin Institute of Technology High-level Teaching Achievement Award(National Level)Cultivation Project(256709).
文摘This paper delves into effective pathways for transforming course ecosystems from resource provision to knowledge service and competency development through university-enterprise collaboration in co-building knowledge graphs and intelligent shared courses.This approach enables personalized,learning-driven teaching.Based on knowledge graphs and integrated teacher-machine-student smart teaching scenarios,it not only innovates autonomous learning environments and human-computer interaction models while optimizing teaching experiences for both instructors and students,but also effectively addresses the issues of students’“scattered,superficial,and fragmented learning”.This establishes the foundation for personalized teaching tailored to individual aptitudes.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12071265,12001481)the Natural Science Foundation of Shandong Province(Grant No.ZR2021MA103)the Youth Innovation Team Project of Shandong Province Universities(Grant No.2024KJG078).
文摘An injective k-edge coloring of a graph G is k-edge coloringκof G such thatκ(e1)≠κ(e3)for any three consecutive edges ei,e2 and e3 of a path or a triangle.The injective chromatic index of G,denoted by x'i(G),is the smallest integer k such that G has an injective k-edge coloring.In this paper,we prove that x'i(G)≤9 if G is a planar graph with maximum degreeΔ≤4,girth g≥6 and without intersecting 6-cycles.
基金supported in part by AFRI grant numbers 2019-7015-29321 and 2021-67015-33409 from the USDA National Institute of Food and Agriculture(NIFA)the SCINet project of the USDA ARS project number 0500-00093-001-00-D。
文摘Structural variations(SVs≥50 bp)are a critical but underexplored source of genetic diversity in cattle,shaping traits vital for productivity,adaptability,and health.Advances in long-read sequencing,pangenome graph construction,and near-complete genome assemblies now allow accurate SV detection and genotyping.These innovations overcome the limitations of single-reference genomes,enabling the discovery of complex SVs,including nested and overlapping variants,and providing access to previously inaccessible genomic regions such as centromeres and telomeres.This review highlights the current landscape of cattle SV research,with emphasis on integrating longread sequencing and pangenome frameworks to uncover breed-specific and population-level variation.While many SVs are linked to economically important traits such as feed efficiency and disease resistance,their broader regulatory impacts remain an active area of investigation.Emerging functional genomics approaches,including transcriptomics,epigenomics,and genome editing,will clarify how SVs influence gene regulation and phenotype.Looking forward,the integration of SV catalogs with multi-omics data,imputation resources,and artificial intelligence-driven models will be essential for translating discoveries into breeding and conservation applications.Integrating structural variants into breeding pipelines promises to revolutionize livestock genomics,enabling precision selection and sustainable agriculture despite challenges in cost,data sharing,and functional validation.
文摘Chain graphs are{2K_(2),C_(3),C_(5)}-free graphs.Balaban index and sum-Balaban index are two important topological indices.In this paper,we concentrate on the subclass of bicyclic connected chain graphs,identifying the extremal graphs that exhibit the minimum or maximum Balaban index and sum-Balaban index within this class.Moreover,we provide a systematic ordering of all bicyclic connected chain graphs according to the magnitude of their Balaban index and sum-Balaban index.
文摘Accurately predicting the synthesizability of inorganic crystal materials serves as a pivotal tool for the efficient screening of viable candidates,substantially reducing the costs associated with extensive experimental trial-and-error processes.However,existing methods,limited by static structural descriptors such as chemical composition and lattice parameters,fail to account for atomic vibrations,which may introduce spurious correlations and undermine predictive reliability.Here,we propose a deep learning model termed integrating graph and dynamical stability(IGDS)for predicting the synthesizability of inorganic crystals.IGDS employs graph representation learning to construct crystal graphs that precisely capture the static structures of crystals and integrates phonon spectral features extracted from pre-trained machine learning interatomic potentials to represent their dynamic properties.Our model exhibits outstanding performance in predicting the synthesizability of low-energy unsynthesizable crystals across 41 material systems,achieving precision and recall values of 0.916/0.863 for ternary compounds.By capturing both static structural descriptors and dynamic features,IGDS provides a physics-informed method for predicting the synthesizability of inorganic crystals.This approach bridges the gap between theoretical design concepts and their practical implementation,thereby streamlining the development cycle of new materials and enhancing overall research efficiency.
基金support from the Scientific Funding for the Center of National Railway Intelligent Transportation System Engineering and Technology,China Academy of Railway Sciences Corporation Limited(Grant No.2023YJ354)。
文摘Knowledge graphs,which combine structured representation with semantic modeling,have shown great potential in knowledge expression,causal inference,and automated reasoning,and are widely used in fields such as intelligent question answering,decision support,and fault diagnosis.As high-speed train systems become increasingly intelligent and interconnected,fault patterns have grown more complex and dynamic.Knowledge graphs offer a promising solution to support the structured management and real-time reasoning of fault knowledge,addressing key requirements such as interpretability,accuracy,and continuous evolution in intelligent diagnostic systems.However,conventional knowledge graph construction relies heavily on domain expertise and specialized tools,resulting in high entry barriers for non-experts and limiting their practical application in frontline maintenance scenarios.To address this limitation,this paper proposes a fault knowledge modeling approach for high-speed trains that integrates structured logic diagrams with knowledge graphs.The method employs a seven-layer logic structure—comprising fault name,applicable vehicles,diagnostic logic,signal parameters,verification conditions,fault causes,and emergency measures—to transform unstructured knowledge into a visual and hierarchical representation.A semantic mapping mechanism is then used to automatically convert logic diagrams into machine-interpretable knowledge graphs,enabling dynamic reasoning and knowledge reuse.Furthermore,the proposed method establishes a three-layer architecture—logic structuring,knowledge graph transformation,and dynamic inference—to bridge human-expert logic with machinebased reasoning.Experimental validation and system implementation demonstrate that this approach not only improves knowledge interpretability and inference precision but also significantly enhances modeling efficiency and system maintainability.It provides a scalable and adaptable solution for intelligent operation and maintenance platforms in the high-speed rail domain.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961041,12261055)the Key Project of Natural Science Foundation of Gansu Province(Grant No.24JRRA222)the Foundation for Innovative Fundamental Research Group Project of Gansu Province(Grant No.25JRRA805).
文摘In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizhong Zhou,Hongxia Liu and Yang Xu(2022).Then,an A_(α)-spectral condition is given to ensure that G is a fractional ID-[a,b]-factor-critical covered graph and an(a,b,k)-factor-critical graph,respectively.In fact,(a,b,k)-factor-critical graph is a graph which has an[a,b]-factor for k=0.Thus,these above results extend the results of Jia Wei and Shenggui Zhang(2023)and Ao Fan,Ruifang Liu and Guoyan Ao(2023)in some sense.
基金Supported by Anhui Provincial Natural Science Foundation(2008085MA06)the Key Project of Anhui Education Committee(gxyqZD2019009)。
文摘Let R be afinite commutative ring with identity 1.The U-clean graph of R,denoted by U-Cl(R),is a graph with vertices in form(e,u),where e is a nonzero idempotent of R and u is a unit of R.In this paper,some basic properties of U-Cl(R)and the explicit structures of U-Cl(Zp×Zq)are given,where p,q are primes.We prove that U-Cl(Zp×Zq)is Eulerlian if and only if p=2,q=2.Moreover,the clique number,the chromatic number of the U-clean graph for some classes of rings are given in this paper.
基金Supported by NSFC(No.12271162)Natural Science Foundation of Shanghai(No.22ZR1416300).
文摘A graph G is H-free,if it contains no H as a subgraph.A graph G is said to be H-minor free,if it does not contain H as a minor.In 2010,Nikiforov asked that what the maximum spectral radius of an H-free graph of order n is.In this paper,we consider some Brualdi-Solheid-Turan type problems on bipartite graphs.In 2015,Zhai,Lin and Gong in[Linear Algebra Appl.,2015,471:21-27]proved that if G is a bipartite graph with order n≥2k+2 and ρ(G)≥ρ(K_(k,n-k)),then G contains a C_(2k+2) unless G≌K_(k,n-k).First,we give a new and more simple proof for the above theorem.Second,we prove that if G is a bipartite graph with order n≥2k+2 and ρ(G)≥ρ(K_(k,n-k)),then G contains all T_(2k+3) unless G≌K_(k,n-k).Finally,we prove that among all outerplanar bipartite graphs on n≥308026 vertices,K_(1,n-1) attains the maximum spectral radius.
基金Supported by the National Natural Science Foundation of China(Nos.12271439,11871398)the National College Students Innovation and Entrepreneurship Training Program(No.201910699173)。
文摘The concept of matching energy was proposed by Gutman and Wagner firstly in 2012. Let G be a simple graph of order n and λ1, λ2, . . . , λn be the zeros of its matching polynomial. The matching energy of a graph G is defined as ME(G) = Pni=1 |λi|. By the famous Coulson’s formula, matching energies can also be calculated by an improper integral depending on a parameter. A k-claw attaching graph Gu(k) refers to the graph obtained by attaching k pendent edges to the graph G at the vertex u, where u is called the root of Gu(k). In this paper, we use some theories of mathematical analysis to obtain a new technique to compare the matching energies of two k-claw attaching graphs Gu(k) and Hv(k) with the same order, that is, limk→∞[ME(Gu(k)) − ME(Hv(k))] = ME(G − u) − ME(H − v). By the technique, we finally determine unicyclic graphs of order n with the 9th to 13th minimal matching energies for all n ≥ 58.
文摘A graph G is called d-degenerate if every subgraph of G has a vertex of degree at most d.It was known that planar graphs are 5-degenerate and every planar graph without k-cycles for some prescribed k∈{3,5,6}is 3-degenerate.In this paper,we show that if G is a planar graph without kites and 9-or 10-cycles,then G is 3-degenerate,hence 4-choosable and list vertex 2-arborable.
文摘A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vertex.This concept was introduced by Tutte as an extension of face colorings,and Tutte in 1954 conjectured that every bridgeless graph admits a nowhere-zero 5-flow,known as the 5-Flow Conjecture.This conjecture is verified for some graph classes and remains unresolved as of today.In this paper,we show that every bridgeless graph of Euler genus at most 20 admits a nowhere-zero 5-flow,which improves several known results.
基金Supported by Changsha Natural Science Foundation(No.kq2208001)the Key Project Funded by Hunan Provincial Department of Education(No.21A0590)。
文摘Determining the crossing number of a given graph is NP-complete. The cycle of length m is denoted by Cm = v1v2…vmv1. G^((1))_(m) (m ≥ 5) is the graph obtained from Cm by adding two edges v1v3 and vlvl+2 (3 ≤ l ≤ m−2), G^((2))m (m ≥ 4) is the graph obtained from Cm by adding two edges v1v3 and v2v4. The famous Zarankiewicz’s conjecture on the crossing number of the complete bipartite graph Km,n states that cr(Km,n)=Z(m,n)=[m/2][m-1/2][n/2[n-1/2].Based on Zarankiewicz’s conjecture, a natural problem is to study the change in the crossingnumber of the graphs obtained from the complete bipartite graph by adding certain edge sets.If Zarankiewicz’s conjecture is true, this paper proves that cr(G^((1))_(m)+Kn)=Z(m,n)+2[n/2] and cr(G^((2))_(m)+Kn)=Z(m,n)+n.
基金Partially supported by NSFC(No.12301436)NSF of Guangxi Province(No.2025GXNSFAA069811)。
文摘DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improves the results of[Discrete Math.,2018,341(7):1983–1986]and[Discrete Appl.Math.,2020,277:245–251].
文摘For a graph G,a vertex is said to be pendant if its neighborhood contains exactly one vertex.In this paper,we determine the extremal graphs among all n-vertex graphs with the minimum spectral radius andβpendant vertices,whereβe{1,2,3,4,n-3,n-2,n-1}.
