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
It is known that long non-coding RNAs(lncRNAs)play vital roles in biological processes and contribute to the progression,development,and treatment of various diseases.Obviously,understanding associations between disea...It is known that long non-coding RNAs(lncRNAs)play vital roles in biological processes and contribute to the progression,development,and treatment of various diseases.Obviously,understanding associations between diseases and lncRNAs significantly enhances our ability to interpret disease mechanisms.Nevertheless,the process of determining lncRNA-disease associations is costly,labor-intensive,and time-consuming.Hence,it is expected to foster computational strategies to uncover lncRNA-disease relationships for further verification to save time and resources.In this study,a collaborative filtering and graph attention network-based LncRNA-Disease Association(CFGANLDA)method was nominated to expose potential lncRNA-disease associations.First,it takes into account the advantages of using biological information from multiple sources.Next,it uses a collaborative filtering technique in order to address the sparse data problem.It also employs a graph attention network to reinforce both linear and non-linear features of the associations to advance prediction performance.The computational results indicate that CFGANLDA gains better prediction performance compared to other state-of-the-art approaches.The CFGANLDA’s area under the receiver operating characteristic curve(AUC)metric is 0.9835,whereas its area under the precision-recall curve(AUPR)metric is 0.9822.Statistical analysis using 10-fold cross-validation experiments proves that these metrics are significant.Furthermore,three case studies on prostate,liver,and stomach cancers attest to the validity of CFGANLDA performance.As a result,CFGANLDA method proves to be a valued tool for lncRNA-disease association prediction.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
Dear Editor,D2This letter presents a node feature similarity preserving graph convolutional framework P G.Graph neural networks(GNNs)have garnered significant attention for their efficacy in learning graph representat...Dear Editor,D2This letter presents a node feature similarity preserving graph convolutional framework P G.Graph neural networks(GNNs)have garnered significant attention for their efficacy in learning graph representations across diverse real-world applications.展开更多
Dear Editor,This letter addresses the critical challenge of preserving privacy in graph learning without compromising on data utility.Differential privacy(DP)is emerging as an effective method for privacy-preserving g...Dear Editor,This letter addresses the critical challenge of preserving privacy in graph learning without compromising on data utility.Differential privacy(DP)is emerging as an effective method for privacy-preserving graph learning.However,its application often diminishes data utility,especially for nodes with fewer neighbors in graph neural networks(GNNs).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.
基金supported by the Vietnam Ministry of Education and Training under project code B2023-SPH-14。
文摘It is known that long non-coding RNAs(lncRNAs)play vital roles in biological processes and contribute to the progression,development,and treatment of various diseases.Obviously,understanding associations between diseases and lncRNAs significantly enhances our ability to interpret disease mechanisms.Nevertheless,the process of determining lncRNA-disease associations is costly,labor-intensive,and time-consuming.Hence,it is expected to foster computational strategies to uncover lncRNA-disease relationships for further verification to save time and resources.In this study,a collaborative filtering and graph attention network-based LncRNA-Disease Association(CFGANLDA)method was nominated to expose potential lncRNA-disease associations.First,it takes into account the advantages of using biological information from multiple sources.Next,it uses a collaborative filtering technique in order to address the sparse data problem.It also employs a graph attention network to reinforce both linear and non-linear features of the associations to advance prediction performance.The computational results indicate that CFGANLDA gains better prediction performance compared to other state-of-the-art approaches.The CFGANLDA’s area under the receiver operating characteristic curve(AUC)metric is 0.9835,whereas its area under the precision-recall curve(AUPR)metric is 0.9822.Statistical analysis using 10-fold cross-validation experiments proves that these metrics are significant.Furthermore,three case studies on prostate,liver,and stomach cancers attest to the validity of CFGANLDA performance.As a result,CFGANLDA method proves to be a valued tool for lncRNA-disease association prediction.
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 by the National Natural Science Foundation of China(62402399)the New Chongqing Youth Innovation Talent Project(CSTB2024NSCQ-QCXMX0035)。
文摘Dear Editor,D2This letter presents a node feature similarity preserving graph convolutional framework P G.Graph neural networks(GNNs)have garnered significant attention for their efficacy in learning graph representations across diverse real-world applications.
基金supported by the National Key Research and Development Program of China(2023YFF0612900,2023YFF0612902)the Natural Science Foundation of Beijing,China(4254086)+3 种基金the National Natural Science Foundation of China(62472032)the Open Project Funding of Key Laboratory of Mobile Application Innovation and Governance Technology,Ministry of Industry and Information Technology(2023IFS080601-K)the Beijing Institute of Technology Research Fund Program for Young Scholarsthe Young Elite Scientists Sponsorship Program by CAST(2023QNRC001)。
文摘Dear Editor,This letter addresses the critical challenge of preserving privacy in graph learning without compromising on data utility.Differential privacy(DP)is emerging as an effective method for privacy-preserving graph learning.However,its application often diminishes data utility,especially for nodes with fewer neighbors in graph neural networks(GNNs).
