Let G be a simple connected graph with n vertices and m edges,L G be the line graph of G and λ 1(L G)≥λ 2(L G)≥...≥λ m(L G) be the eigenvalues of the graph L G.In this paper,the range of eigenvalues of a...Let G be a simple connected graph with n vertices and m edges,L G be the line graph of G and λ 1(L G)≥λ 2(L G)≥...≥λ m(L G) be the eigenvalues of the graph L G.In this paper,the range of eigenvalues of a line graph is considered.Some sharp upper bounds and sharp lower bounds of the eigenvalues of L G are obtained.In particular,it is proved that-2cos(πn)≤λ n-1 (L G)≤n-4 and λ n(L G)=-2 if and only if G is bipartite.展开更多
In this paper,we give a necessary and sufficient condition for the existence of P3-factors in the line graph of a tree.Then we present an algorithm to determine whether the line graph of a tree has a P3-factor.
This paper shows that if G is a connected graph of order n such that <(sigma(2)(G))over bar> > 2(n/5 - 1) and L(G) is hamiltonian, then, for n greater than or equal to 43, L(G) is pancyclic. Using the result ...This paper shows that if G is a connected graph of order n such that <(sigma(2)(G))over bar> > 2(n/5 - 1) and L(G) is hamiltonian, then, for n greater than or equal to 43, L(G) is pancyclic. Using the result of Veldman([8]) this result settles the conjecture of Benhocine, et.al([1]): Let G be a connected almost bridgeless graph of order n such that <(sigma(2)(G))over bar> > 2(n/5 - 1). If n is sufficintly large, L(G) is pancyclic.展开更多
A signed graph S=(S^(u),σ)has an underlying graph Suand a functionσ:E(S^(u))-→{+,-}.Let E^(-)(S)denote the set of negative edges of S.Then S is eulerian signed graph(or subeulerian signed graph,or balanced eulerian...A signed graph S=(S^(u),σ)has an underlying graph Suand a functionσ:E(S^(u))-→{+,-}.Let E^(-)(S)denote the set of negative edges of S.Then S is eulerian signed graph(or subeulerian signed graph,or balanced eulerian signed graph,respectively)if Suis eulerian(or subeulerian,or eulerian and|E-(S)|is even,respectively).We say that S is balanced subeulerian signed graph if there exists a balanced eulerian signed graph S′such that S′is spanned by S.The signed line graph L(S)of a signed graph S is a signed graph with the vertices of L(S)being the edges of S,where an edge eiej is in L(S)if and only if the edges e_(i)and e_(j)of S have a vertex in common in S such that an edge eiej in L(S)is negative if and only if both edges ei and ej are negative in S.In this paper,two families of signed graphs S and S′are identified,which are applied to characterize balanced subeulerian signed graphs and balanced subeulerian signed line graphs.In particular,it is proved that a signed graph S is balanced subeulerian if and only if S∈S,and that a signed line graph of signed graph S is balanced subeulerian if and only if S∈S′.展开更多
The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability indices than the conneetivity and the edge-connectivity. This paper shows that for a connected balanced digraph D...The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability indices than the conneetivity and the edge-connectivity. This paper shows that for a connected balanced digraph D and its line digraph L, if D is optimally super edge-connected, then κ1（L） = 2λ1 （D）, and that for a connected graph G and its line graph L, if one of κ1 （L） and λ（G） exists, then κ1（L） = λ2（G）. This paper determines that κ1（B（d, n） is equal to 4d- 8 for n = 2 and d ≥ 4, and to 4d-4 for n ≥ 3 and d ≥ 3, and that κ1（K（d, n）） is equal to 4d- 4 for d 〉 2 and n ≥ 2 except K（2, 2）. It then follows that B（d,n） and K（d, n） are both super connected for any d ≥ 2 and n ≥ 1.展开更多
We consider even factors with a bounded number of components in the n-times iterated line graphs L^n(G). We present a characterization of a simple graph G such that L^n(G) has an even factor with at most k components,...We consider even factors with a bounded number of components in the n-times iterated line graphs L^n(G). We present a characterization of a simple graph G such that L^n(G) has an even factor with at most k components, based on the existence of a certain type of subgraphs in G. Moreover, we use this result to give some upper bounds for the minimum number of components of even factors in L^n(G) and also show that the minimum number of components of even factors in L^n(G) is stable under the closure operation on a claw-free graph G, which extends some known results. Our results show that it seems to be NP-hard to determine the minimum number of components of even factors of iterated line graphs. We also propose some problems for further research.展开更多
Let G be a multigraph.Suppose that e=u1v1 and e′=u2v2 are two edges of G.If e≠e′,then G(e,e′)is the graph obtained from G by replacing e=u1v1 with a path u1vev1 and by replacing e′=u2v2 with a path u2ve′v2,where...Let G be a multigraph.Suppose that e=u1v1 and e′=u2v2 are two edges of G.If e≠e′,then G(e,e′)is the graph obtained from G by replacing e=u1v1 with a path u1vev1 and by replacing e′=u2v2 with a path u2ve′v2,where ve,ve′are two new vertices not in V(G).If e=e′,then G(e,e′),also denoted by G(e),is obtained from G by replacing e=u1v1 with a path u1vev1.A graph G is strongly spanning trailable if for any e,e′∈E(G),G(e,e′)has a spanning(ve,ve′)-trail.The design of n processor network with given number of connections from each processor and with a desirable strength of the network can be modelled as a degree sequence realization problem with certain desirable graphical properties.A sequence d=(d1,d2,⋯,dn)is multigraphic if there is a multigraph G with degree sequence d,and such a graph G is called a realization of d.A multigraphic degree sequence d is strongly spanning trailable if d has a realization G which is a strongly spanning trailable graph,and d is line-hamiltonian-connected if d has a realization G such that the line graph of G is hamiltonian-connected.In this paper,we prove that a nonincreasing multigraphic sequence d=(d1,d2)⋯,dn)is strongly spanning trailable if and only if either n=1 and d1=0 or n≥2 and dn≥3.Applying this result,we prove that for a nonincreasing multigraphic sequence d=(d1,d2,⋯,dn),if n≥2 and dn≥3,then d is line-hamiltonian-connected.展开更多
The Wiener index W(G)of a graph G is a distance-based topological index defined as the sum of distances between all pairs of vertices in G.It is shown that forλ=2 there is an infinite family of planar bipartite chemi...The Wiener index W(G)of a graph G is a distance-based topological index defined as the sum of distances between all pairs of vertices in G.It is shown that forλ=2 there is an infinite family of planar bipartite chemical graphs G of girth 4 with the cyclomatic numberλ,but their line graphs are not chemical graphs,and forλ≥2 there are two infinite families of planar nonbipartite graphs G of girth 3 with the cyclomatic numberλ;the three classes of graphs have the property W(G)=W(L(G)),where L(G)is the line graph of G.展开更多
In this paper,we prove that L(K_(x,y))(λ),theλ-fold line graph of the complete bipartite graph Ka,y,has a C_(6)-decomposition if and only if ry≥6,λxy(c+y-2)=0(mod 12)and(x+y)=0(mod 2),where x,y are nonnegative int...In this paper,we prove that L(K_(x,y))(λ),theλ-fold line graph of the complete bipartite graph Ka,y,has a C_(6)-decomposition if and only if ry≥6,λxy(c+y-2)=0(mod 12)and(x+y)=0(mod 2),where x,y are nonnegative integers and(x,y)≠(2,4)or(2,5).展开更多
For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which ...For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which are distance two apart receive labels differing by at least k. The λ′j,k-number of G is the minimum m of an m-L（j, k）-edge-labeling admitted by G.In this article, we study the L（1, 2）-edge-labeling for paths, cycles, complete graphs, complete multipartite graphs, infinite ？-regular trees and wheels.展开更多
A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant A such that the equality λd（ui） = ∑（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,…, ｜V（G）｜, where d（vi） denotes the degr...A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant A such that the equality λd（ui） = ∑（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,…, ｜V（G）｜, where d（vi） denotes the degree of vertex vi. In this paper, some harmonic properties of the complement and line graph are given, and some algebraic properties for the λ-Hgraphs are obtained.展开更多
Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characteri...Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.展开更多
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
The increasing popularity of the Internet and the widespread use of information technology have led to a rise in the number and sophistication of network attacks and security threats.Intrusion detection systems are cr...The increasing popularity of the Internet and the widespread use of information technology have led to a rise in the number and sophistication of network attacks and security threats.Intrusion detection systems are crucial to network security,playing a pivotal role in safeguarding networks from potential threats.However,in the context of an evolving landscape of sophisticated and elusive attacks,existing intrusion detection methodologies often overlook critical aspects such as changes in network topology over time and interactions between hosts.To address these issues,this paper proposes a real-time network intrusion detection method based on graph neural networks.The proposedmethod leverages the advantages of graph neural networks and employs a straightforward graph construction method to represent network traffic as dynamic graph-structured data.Additionally,a graph convolution operation with a multi-head attention mechanism is utilized to enhance the model’s ability to capture the intricate relationships within the graph structure comprehensively.Furthermore,it uses an integrated graph neural network to address dynamic graphs’structural and topological changes at different time points and the challenges of edge embedding in intrusion detection data.The edge classification problem is effectively transformed into node classification by employing a line graph data representation,which facilitates fine-grained intrusion detection tasks on dynamic graph node feature representations.The efficacy of the proposed method is evaluated using two commonly used intrusion detection datasets,UNSW-NB15 and NF-ToN-IoT-v2,and results are compared with previous studies in this field.The experimental results demonstrate that our proposed method achieves 99.3%and 99.96%accuracy on the two datasets,respectively,and outperforms the benchmark model in several evaluation metrics.展开更多
The Jing-well point temperatures test method is a method to diagnose and guide the treatment of diseases by measuring the subjects' symmetrical well point temperature. it is improved from the method of knowing hea...The Jing-well point temperatures test method is a method to diagnose and guide the treatment of diseases by measuring the subjects' symmetrical well point temperature. it is improved from the method of knowing heat sensitivity. The application of Jing-well point temperatures test method is wide, and it can be used in internal and external gynecology and pediatrics and facial features department. at the same time, it has the advantage of objective and accurate diagnosis. The old law has some shortcomings, such as poor intuition, unavoidable omission of information, incomplete interpretation of information and so on. In this paper, Excel software is used to transform the data into line chart form, which improves the intuition and comprehensiveness of this method, so that the data can be better interpreted and used. It is newly proposed in this article that in addition to observing the longitudinal di fference of well point temperature, more attention should be paid to the horizontal contrast difference of well point temperature in different meridians. The article also summarizes a number of treatment methods, including acupuncture, moxa moxibustion, cupping and scraping, and the selection of acupoints, including mother acupoints, tenderness points and heat-sensitive moxibustion, so that doctors can combine traditional Chinese medicine professional knowledge in clinic.展开更多
Two methods for determining the supereulerian index of a graph G are given. A sharp upper bound and a sharp lower bound on the supereulerian index by studying the branch bonds of G are got.
In this note,we show a sharp lower bound of min{Σ_(i=1)^(k)dG(u_(i)):u1u2...uk is a path of(2-)connected G}on its order such that(k-1)-iterated line graphs L^(k-1)(G)are hamiltonian.
For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edg...For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edges which are distance two apart receive labels differ at least by k. The λj,k-number of G is the minimum m such that an m-L（j, k）-edge-labeling is admitted by G. In this article, the L（1, 2）-edge-labeling for the hexagonal lattice, the square lattice and the triangular lattice are studied, and the bounds for λj,k-numbers of these graphs are obtained.展开更多
BACKGROUND Gastric cancer is a leading cause of cancer-related deaths worldwide.Prognostic assessments are typically based on the tumor-node-metastasis(TNM)staging system,which does not account for the molecular heter...BACKGROUND Gastric cancer is a leading cause of cancer-related deaths worldwide.Prognostic assessments are typically based on the tumor-node-metastasis(TNM)staging system,which does not account for the molecular heterogeneity of this disease.LATS2,a tumor suppressor gene involved in the Hippo signaling pathway,has been identified as a potential prognostic biomarker in gastric cancer.AIM To construct and validate a nomogram model that includes LATS2 expression to predict the survival prognosis of advanced gastric cancer patients following ra-dical surgery,and compare its predictive performance with traditional TNM staging.METHODS A retrospective analysis of 245 advanced gastric cancer patients from the Fourth Hospital of Hebei Medical University was conducted.The patients were divided into a training group(171 patients)and a validation group(74 patients)to deve-lop and test our prognostic model.The performance of the model was determined using C-indices,receiver operating characteristic curves,calibration plots,and decision curves.RESULTS The model demonstrated a high predictive accuracy with C-indices of 0.829 in the training set and 0.862 in the validation set.Area under the curve values for three-year and five-year survival prediction were significantly robust,suggesting an excellent discrimination ability.Calibration plots confirmed the high concordance between the predictions and actual survival outcomes.CONCLUSION We developed a nomogram model incorporating LATS2 expression,which significantly outperformed conven-tional TNM staging in predicting the prognosis of advanced gastric cancer patients postsurgery.This model may serve as a valuable tool for individualized patient management,allowing for more accurate stratification and im-proved clinical outcomes.Further validation in larger patient cohorts will be necessary to establish its generaliza-bility and clinical utility.展开更多
文摘Let G be a simple connected graph with n vertices and m edges,L G be the line graph of G and λ 1(L G)≥λ 2(L G)≥...≥λ m(L G) be the eigenvalues of the graph L G.In this paper,the range of eigenvalues of a line graph is considered.Some sharp upper bounds and sharp lower bounds of the eigenvalues of L G are obtained.In particular,it is proved that-2cos(πn)≤λ n-1 (L G)≤n-4 and λ n(L G)=-2 if and only if G is bipartite.
文摘In this paper,we give a necessary and sufficient condition for the existence of P3-factors in the line graph of a tree.Then we present an algorithm to determine whether the line graph of a tree has a P3-factor.
文摘This paper shows that if G is a connected graph of order n such that <(sigma(2)(G))over bar> > 2(n/5 - 1) and L(G) is hamiltonian, then, for n greater than or equal to 43, L(G) is pancyclic. Using the result of Veldman([8]) this result settles the conjecture of Benhocine, et.al([1]): Let G be a connected almost bridgeless graph of order n such that <(sigma(2)(G))over bar> > 2(n/5 - 1). If n is sufficintly large, L(G) is pancyclic.
基金Supported by the National Natural Science Foundation of China(Grant No.12261016)。
文摘A signed graph S=(S^(u),σ)has an underlying graph Suand a functionσ:E(S^(u))-→{+,-}.Let E^(-)(S)denote the set of negative edges of S.Then S is eulerian signed graph(or subeulerian signed graph,or balanced eulerian signed graph,respectively)if Suis eulerian(or subeulerian,or eulerian and|E-(S)|is even,respectively).We say that S is balanced subeulerian signed graph if there exists a balanced eulerian signed graph S′such that S′is spanned by S.The signed line graph L(S)of a signed graph S is a signed graph with the vertices of L(S)being the edges of S,where an edge eiej is in L(S)if and only if the edges e_(i)and e_(j)of S have a vertex in common in S such that an edge eiej in L(S)is negative if and only if both edges ei and ej are negative in S.In this paper,two families of signed graphs S and S′are identified,which are applied to characterize balanced subeulerian signed graphs and balanced subeulerian signed line graphs.In particular,it is proved that a signed graph S is balanced subeulerian if and only if S∈S,and that a signed line graph of signed graph S is balanced subeulerian if and only if S∈S′.
基金Supported by the National Natural Science Foundation of China(No.10271114,No.10301031).
文摘The h-super connectivity κh and the h-super edge-connectivity λh are more refined network reliability indices than the conneetivity and the edge-connectivity. This paper shows that for a connected balanced digraph D and its line digraph L, if D is optimally super edge-connected, then κ1（L） = 2λ1 （D）, and that for a connected graph G and its line graph L, if one of κ1 （L） and λ（G） exists, then κ1（L） = λ2（G）. This paper determines that κ1（B（d, n） is equal to 4d- 8 for n = 2 and d ≥ 4, and to 4d-4 for n ≥ 3 and d ≥ 3, and that κ1（K（d, n）） is equal to 4d- 4 for d 〉 2 and n ≥ 2 except K（2, 2）. It then follows that B（d,n） and K（d, n） are both super connected for any d ≥ 2 and n ≥ 1.
基金supported by National Natural Science Foundation of China (Grant Nos. 11471037 and 11171129)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20131101110048)
文摘We consider even factors with a bounded number of components in the n-times iterated line graphs L^n(G). We present a characterization of a simple graph G such that L^n(G) has an even factor with at most k components, based on the existence of a certain type of subgraphs in G. Moreover, we use this result to give some upper bounds for the minimum number of components of even factors in L^n(G) and also show that the minimum number of components of even factors in L^n(G) is stable under the closure operation on a claw-free graph G, which extends some known results. Our results show that it seems to be NP-hard to determine the minimum number of components of even factors of iterated line graphs. We also propose some problems for further research.
基金This paper is supported by the National Natural Science Foundation of China(Nos.11771039,11971054)Fundamental Research Funds for the Central Universities of China(No.2015JBM107)the 111 Project of China(No.B16002)。
文摘Let G be a multigraph.Suppose that e=u1v1 and e′=u2v2 are two edges of G.If e≠e′,then G(e,e′)is the graph obtained from G by replacing e=u1v1 with a path u1vev1 and by replacing e′=u2v2 with a path u2ve′v2,where ve,ve′are two new vertices not in V(G).If e=e′,then G(e,e′),also denoted by G(e),is obtained from G by replacing e=u1v1 with a path u1vev1.A graph G is strongly spanning trailable if for any e,e′∈E(G),G(e,e′)has a spanning(ve,ve′)-trail.The design of n processor network with given number of connections from each processor and with a desirable strength of the network can be modelled as a degree sequence realization problem with certain desirable graphical properties.A sequence d=(d1,d2,⋯,dn)is multigraphic if there is a multigraph G with degree sequence d,and such a graph G is called a realization of d.A multigraphic degree sequence d is strongly spanning trailable if d has a realization G which is a strongly spanning trailable graph,and d is line-hamiltonian-connected if d has a realization G such that the line graph of G is hamiltonian-connected.In this paper,we prove that a nonincreasing multigraphic sequence d=(d1,d2)⋯,dn)is strongly spanning trailable if and only if either n=1 and d1=0 or n≥2 and dn≥3.Applying this result,we prove that for a nonincreasing multigraphic sequence d=(d1,d2,⋯,dn),if n≥2 and dn≥3,then d is line-hamiltonian-connected.
基金This work was supported by the National Natural Science Foundation of China(No.11171273)The authors would like to express their sincere gratitude to the anonymous referees for their comments and remarks,which improved the presentation of this paper.
文摘The Wiener index W(G)of a graph G is a distance-based topological index defined as the sum of distances between all pairs of vertices in G.It is shown that forλ=2 there is an infinite family of planar bipartite chemical graphs G of girth 4 with the cyclomatic numberλ,but their line graphs are not chemical graphs,and forλ≥2 there are two infinite families of planar nonbipartite graphs G of girth 3 with the cyclomatic numberλ;the three classes of graphs have the property W(G)=W(L(G)),where L(G)is the line graph of G.
文摘In this paper,we prove that L(K_(x,y))(λ),theλ-fold line graph of the complete bipartite graph Ka,y,has a C_(6)-decomposition if and only if ry≥6,λxy(c+y-2)=0(mod 12)and(x+y)=0(mod 2),where x,y are nonnegative integers and(x,y)≠(2,4)or(2,5).
基金Supported by the National Natural Science Foundation of China(Grant Nos.1097102510901035)
文摘For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which are distance two apart receive labels differing by at least k. The λ′j,k-number of G is the minimum m of an m-L（j, k）-edge-labeling admitted by G.In this article, we study the L（1, 2）-edge-labeling for paths, cycles, complete graphs, complete multipartite graphs, infinite ？-regular trees and wheels.
基金supported by the fund of South China Agricultural University (4900-K08225)supported by the National Natural Science Foundation of China(10771080)Specialized Research Fund for the Doctoral Program of Higher Eduction (20070574006)
文摘A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant A such that the equality λd（ui） = ∑（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,…, ｜V（G）｜, where d（vi） denotes the degree of vertex vi. In this paper, some harmonic properties of the complement and line graph are given, and some algebraic properties for the λ-Hgraphs are obtained.
基金Supported by the Natural Science Foundation of China(12131013,12371356)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002015)the Fundamental Research Program of Shanxi Province(202303021221064).
文摘Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.
基金Supported by the National Natural Science Foundation of China (Grant No. 10961023)National Natural Science Foundation of China for Young Scholars (Grant No. 11101232)+1 种基金Natural Science Foundation of Qinghai Province for Young Scholars (Grant No. 2011-Z-929Q)Scientific Research Innovation Program of Qinghai Normal University
文摘In the paper, we prove that all generalized cocktail-party graphs with order at least 23 are determined by their adjacency spectra.
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The increasing popularity of the Internet and the widespread use of information technology have led to a rise in the number and sophistication of network attacks and security threats.Intrusion detection systems are crucial to network security,playing a pivotal role in safeguarding networks from potential threats.However,in the context of an evolving landscape of sophisticated and elusive attacks,existing intrusion detection methodologies often overlook critical aspects such as changes in network topology over time and interactions between hosts.To address these issues,this paper proposes a real-time network intrusion detection method based on graph neural networks.The proposedmethod leverages the advantages of graph neural networks and employs a straightforward graph construction method to represent network traffic as dynamic graph-structured data.Additionally,a graph convolution operation with a multi-head attention mechanism is utilized to enhance the model’s ability to capture the intricate relationships within the graph structure comprehensively.Furthermore,it uses an integrated graph neural network to address dynamic graphs’structural and topological changes at different time points and the challenges of edge embedding in intrusion detection data.The edge classification problem is effectively transformed into node classification by employing a line graph data representation,which facilitates fine-grained intrusion detection tasks on dynamic graph node feature representations.The efficacy of the proposed method is evaluated using two commonly used intrusion detection datasets,UNSW-NB15 and NF-ToN-IoT-v2,and results are compared with previous studies in this field.The experimental results demonstrate that our proposed method achieves 99.3%and 99.96%accuracy on the two datasets,respectively,and outperforms the benchmark model in several evaluation metrics.
文摘The Jing-well point temperatures test method is a method to diagnose and guide the treatment of diseases by measuring the subjects' symmetrical well point temperature. it is improved from the method of knowing heat sensitivity. The application of Jing-well point temperatures test method is wide, and it can be used in internal and external gynecology and pediatrics and facial features department. at the same time, it has the advantage of objective and accurate diagnosis. The old law has some shortcomings, such as poor intuition, unavoidable omission of information, incomplete interpretation of information and so on. In this paper, Excel software is used to transform the data into line chart form, which improves the intuition and comprehensiveness of this method, so that the data can be better interpreted and used. It is newly proposed in this article that in addition to observing the longitudinal di fference of well point temperature, more attention should be paid to the horizontal contrast difference of well point temperature in different meridians. The article also summarizes a number of treatment methods, including acupuncture, moxa moxibustion, cupping and scraping, and the selection of acupoints, including mother acupoints, tenderness points and heat-sensitive moxibustion, so that doctors can combine traditional Chinese medicine professional knowledge in clinic.
文摘Two methods for determining the supereulerian index of a graph G are given. A sharp upper bound and a sharp lower bound on the supereulerian index by studying the branch bonds of G are got.
基金Supported by the National Natural Science Foundation of China(11871099).
文摘In this note,we show a sharp lower bound of min{Σ_(i=1)^(k)dG(u_(i)):u1u2...uk is a path of(2-)connected G}on its order such that(k-1)-iterated line graphs L^(k-1)(G)are hamiltonian.
基金Supported by the National Natural Science Foundation of China(10971025 and 10901035)
文摘For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edges which are distance two apart receive labels differ at least by k. The λj,k-number of G is the minimum m such that an m-L（j, k）-edge-labeling is admitted by G. In this article, the L（1, 2）-edge-labeling for the hexagonal lattice, the square lattice and the triangular lattice are studied, and the bounds for λj,k-numbers of these graphs are obtained.
文摘BACKGROUND Gastric cancer is a leading cause of cancer-related deaths worldwide.Prognostic assessments are typically based on the tumor-node-metastasis(TNM)staging system,which does not account for the molecular heterogeneity of this disease.LATS2,a tumor suppressor gene involved in the Hippo signaling pathway,has been identified as a potential prognostic biomarker in gastric cancer.AIM To construct and validate a nomogram model that includes LATS2 expression to predict the survival prognosis of advanced gastric cancer patients following ra-dical surgery,and compare its predictive performance with traditional TNM staging.METHODS A retrospective analysis of 245 advanced gastric cancer patients from the Fourth Hospital of Hebei Medical University was conducted.The patients were divided into a training group(171 patients)and a validation group(74 patients)to deve-lop and test our prognostic model.The performance of the model was determined using C-indices,receiver operating characteristic curves,calibration plots,and decision curves.RESULTS The model demonstrated a high predictive accuracy with C-indices of 0.829 in the training set and 0.862 in the validation set.Area under the curve values for three-year and five-year survival prediction were significantly robust,suggesting an excellent discrimination ability.Calibration plots confirmed the high concordance between the predictions and actual survival outcomes.CONCLUSION We developed a nomogram model incorporating LATS2 expression,which significantly outperformed conven-tional TNM staging in predicting the prognosis of advanced gastric cancer patients postsurgery.This model may serve as a valuable tool for individualized patient management,allowing for more accurate stratification and im-proved clinical outcomes.Further validation in larger patient cohorts will be necessary to establish its generaliza-bility and clinical utility.
