All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting ...All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.展开更多
A sensor graph network is a sensor network model organized according to graph network structure.Structural unit and signal propagation of core nodes are the basic characteristics of sensor graph networks.In sensor net...A sensor graph network is a sensor network model organized according to graph network structure.Structural unit and signal propagation of core nodes are the basic characteristics of sensor graph networks.In sensor networks,network structure recognition is the basis for accurate identification and effective prediction and control of node states.Aiming at the problems of difficult global structure identification and poor interpretability in complex sensor graph networks,based on the characteristics of sensor networks,a method is proposed to firstly unitize the graph network structure and then expand the unit based on the signal transmission path of the core node.This method which builds on unit patulousness and core node signal propagation(called p-law)can rapidly and effectively achieve the global structure identification of a sensor graph network.Different from the traditional graph network structure recognition algorithms such as modularity maximization and spectral clustering,the proposed method reveals the natural evolution process and law of graph network subgroup generation.Experimental results confirm the effectiveness,accuracy and rationality of the proposed method and suggest that our method can be a new approach for graph network global structure recognition.展开更多
In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then ...In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then G is isomorphic to M if and only if the set of the orders of the maximal abelian subgoups of G is the same as that of M .展开更多
Let G be a finite group and N a normal subgroup of G.Denote by Γ_(G)(N)the graph whose vertices are all distinct G-conjugacy class sizes of non-central elements in N,and two vertices of Γ_(G)(N)are adjacent if and o...Let G be a finite group and N a normal subgroup of G.Denote by Γ_(G)(N)the graph whose vertices are all distinct G-conjugacy class sizes of non-central elements in N,and two vertices of Γ_(G)(N)are adjacent if and only if they are not coprime numbers.We prove that if the center Z(N)=Z(G)∩N and Γ_(G)(N)is k-regular for k≥1,then either a section of Nis a quasi-Frobenius group or Γ_(G)(N)is a complete graph with k+1 vertices.展开更多
基金The NSF (60776810,10871205) of Chinathe NSF (08JCYBJC13900) of Tianjin
文摘All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.
基金This research is supported by the Natural Science Foundation Project of Fujian Provincial Department of Science and Technology(Grant No.2020J01385)Digital Fujian Industrial Energy Big Data Research Institute(Grant No.KB180045)Provincial Key Laboratory of Industrial Big Data Analysis and Application(Grant No.KB180029).
文摘A sensor graph network is a sensor network model organized according to graph network structure.Structural unit and signal propagation of core nodes are the basic characteristics of sensor graph networks.In sensor networks,network structure recognition is the basis for accurate identification and effective prediction and control of node states.Aiming at the problems of difficult global structure identification and poor interpretability in complex sensor graph networks,based on the characteristics of sensor networks,a method is proposed to firstly unitize the graph network structure and then expand the unit based on the signal transmission path of the core node.This method which builds on unit patulousness and core node signal propagation(called p-law)can rapidly and effectively achieve the global structure identification of a sensor graph network.Different from the traditional graph network structure recognition algorithms such as modularity maximization and spectral clustering,the proposed method reveals the natural evolution process and law of graph network subgroup generation.Experimental results confirm the effectiveness,accuracy and rationality of the proposed method and suggest that our method can be a new approach for graph network global structure recognition.
文摘In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then G is isomorphic to M if and only if the set of the orders of the maximal abelian subgoups of G is the same as that of M .
基金partially supported by the National Natural Science Foundation of China(11901169)the Youth Science Foundation of Henan Normal University(2019QK02)the Project for Graduate Education Reform and Quality Improvement of Henan Province and Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control,College of Mathematics and Information Science.
文摘Let G be a finite group and N a normal subgroup of G.Denote by Γ_(G)(N)the graph whose vertices are all distinct G-conjugacy class sizes of non-central elements in N,and two vertices of Γ_(G)(N)are adjacent if and only if they are not coprime numbers.We prove that if the center Z(N)=Z(G)∩N and Γ_(G)(N)is k-regular for k≥1,then either a section of Nis a quasi-Frobenius group or Γ_(G)(N)is a complete graph with k+1 vertices.
