Diagnosability of a multiprocessor system is one important study topic. In 2015, Zhang et al. proposed a new measure for fault diagnosis of the system, namely, g-extra diagnosability, which restrains that every fault-...Diagnosability of a multiprocessor system is one important study topic. In 2015, Zhang et al. proposed a new measure for fault diagnosis of the system, namely, g-extra diagnosability, which restrains that every fault-free component has at least (g + 1) fault-free nodes. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph AGn has many good properties. In this paper, we give that the 2-extra diagnosability of AGn is 6n - 17 for n≥ 5 under the PMC model and MM* model.展开更多
It is difficult to rescue people from outside, and emergency evacuation is still a main measure to decrease casualties in high-rise building fires. To improve evacuation efficiency, a valid and easily manipulated grou...It is difficult to rescue people from outside, and emergency evacuation is still a main measure to decrease casualties in high-rise building fires. To improve evacuation efficiency, a valid and easily manipulated grouping evacuation strategy is proposed. Occupants escape in groups according to the shortest evacuation route is determined by graph theory. In order to evaluate and find the optimal grouping, computational experiments are performed to design and simulate the evacuation processes. A case study shown the application in detail and quantitative research conclusions is obtained. The thoughts and approaches of this study can be used to guide actual high-rise building evacuation processes in future.展开更多
The commuting graph of an arbitrary ring R, denoted by Г（R）, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we inv...The commuting graph of an arbitrary ring R, denoted by Г（R）, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity and the diameter of Г（ZnS3）. We show that Г（ZnS3） is connected if and only if n is not a prime number. If Г（ZnS3） is connected then diam（Г（ZnS3）） = 3, while ifГ（ZnS3） is disconnected then every connected component of Г（ZnS3） must be a complete graph with same size, and we completely determine the vertice set of every connected component.展开更多
Let S\-n be the symmetric group, g\++\-i=(123i),g\+-\-i=(1i32) and M\++\-n={g\++\-i∶4≤i≤n}, then M\++\-n is a minimal generating set of S\-n ,where n ≥5.It is proved that Cayley graph Cay( S\-...Let S\-n be the symmetric group, g\++\-i=(123i),g\+-\-i=(1i32) and M\++\-n={g\++\-i∶4≤i≤n}, then M\++\-n is a minimal generating set of S\-n ,where n ≥5.It is proved that Cayley graph Cay( S\-n,M\++\-n∪M\+-\-n) is Hamiltonian and edge symmetric.展开更多
In this paper, sharp upper bounds for the domination number, total domination number and connected domination number for the Cayley graph G = Cay(D2n, Ω) constructed on the finite dihedral group D2n, and a specified ...In this paper, sharp upper bounds for the domination number, total domination number and connected domination number for the Cayley graph G = Cay(D2n, Ω) constructed on the finite dihedral group D2n, and a specified generating set Ω of D2n. Further efficient dominating sets in G = Cay(D2n, Ω) are also obtained. More specifically, it is proved that some of the proper subgroups of D2n are efficient domination sets. Using this, an E-chain of Cayley graphs on the dihedral group is also constructed.展开更多
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
In this paper, we mainly study the orbital graphs of primitive groups with the socle A<sub>7</sub> x A<sub>7 </sub>which acts by diagonal action. Firstly, we calculate the element conjugat...In this paper, we mainly study the orbital graphs of primitive groups with the socle A<sub>7</sub> x A<sub>7 </sub>which acts by diagonal action. Firstly, we calculate the element conjugate classes of A7</sub>, then we discuss the stabilizer of two points in A7</sub>. Finally, according to the relation between suborbit and orbital, we obtain the orbitals, and determine the orbital graphs.展开更多
Let G be a finite group and π（G） = {pl,p2,…… ,pk} be the set of the primes dividing the order of G. We define its prime graph F（G） as follows. The vertex set of this graph is 7r（G）, and two distinct vertices ...Let G be a finite group and π（G） = {pl,p2,…… ,pk} be the set of the primes dividing the order of G. We define its prime graph F（G） as follows. The vertex set of this graph is 7r（G）, and two distinct vertices p, q are joined by an edge if and only if pq ∈ πe（G）. In this case, we write p - q. For p ∈π（G）, put deg（p） ：= ｜{q ∈ π（G）｜p - q}｜, which is called the degree of p. We also define D（G） ：= （deg（p1）, deg（p2）,..., deg（pk））, where pl 〈 p2 〈 -……〈 pk, which is called the degree pattern of G. We say a group G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and degree pattern as G. Specially, a l-fold OD-characterizable group is simply called an OD-characterizable group. Let L ：= U6（2）. In this article, we classify all finite groups with the same order and degree pattern as an almost simple groups related to L. In fact, we prove that L and L.2 are OD-characterizable, L.3 is 3-fold OD-characterizable, and L.S3 is 5-fold OD-characterizable.展开更多
文摘Diagnosability of a multiprocessor system is one important study topic. In 2015, Zhang et al. proposed a new measure for fault diagnosis of the system, namely, g-extra diagnosability, which restrains that every fault-free component has at least (g + 1) fault-free nodes. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph AGn has many good properties. In this paper, we give that the 2-extra diagnosability of AGn is 6n - 17 for n≥ 5 under the PMC model and MM* model.
基金supported by Beijing University of Civil Engineering and Architecture Nature Science(ZF16078,X18067)
文摘It is difficult to rescue people from outside, and emergency evacuation is still a main measure to decrease casualties in high-rise building fires. To improve evacuation efficiency, a valid and easily manipulated grouping evacuation strategy is proposed. Occupants escape in groups according to the shortest evacuation route is determined by graph theory. In order to evaluate and find the optimal grouping, computational experiments are performed to design and simulate the evacuation processes. A case study shown the application in detail and quantitative research conclusions is obtained. The thoughts and approaches of this study can be used to guide actual high-rise building evacuation processes in future.
基金The NSF(10971024)of Chinathe Specialized Research Fund(200802860024)for the Doctoral Program of Higher Educationthe NSF(BK2010393)of Jiangsu Province
文摘The commuting graph of an arbitrary ring R, denoted by Г（R）, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity and the diameter of Г（ZnS3）. We show that Г（ZnS3） is connected if and only if n is not a prime number. If Г（ZnS3） is connected then diam（Г（ZnS3）） = 3, while ifГ（ZnS3） is disconnected then every connected component of Г（ZnS3） must be a complete graph with same size, and we completely determine the vertice set of every connected component.
文摘Let S\-n be the symmetric group, g\++\-i=(123i),g\+-\-i=(1i32) and M\++\-n={g\++\-i∶4≤i≤n}, then M\++\-n is a minimal generating set of S\-n ,where n ≥5.It is proved that Cayley graph Cay( S\-n,M\++\-n∪M\+-\-n) is Hamiltonian and edge symmetric.
文摘In this paper, sharp upper bounds for the domination number, total domination number and connected domination number for the Cayley graph G = Cay(D2n, Ω) constructed on the finite dihedral group D2n, and a specified generating set Ω of D2n. Further efficient dominating sets in G = Cay(D2n, Ω) are also obtained. More specifically, it is proved that some of the proper subgroups of D2n are efficient domination sets. Using this, an E-chain of Cayley graphs on the dihedral group is also constructed.
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.
文摘In this paper, we mainly study the orbital graphs of primitive groups with the socle A<sub>7</sub> x A<sub>7 </sub>which acts by diagonal action. Firstly, we calculate the element conjugate classes of A7</sub>, then we discuss the stabilizer of two points in A7</sub>. Finally, according to the relation between suborbit and orbital, we obtain the orbitals, and determine the orbital graphs.
基金supported by Natural Science Foundation Project of CQ CSTC (2010BB9206)NNSF of China (10871032)+1 种基金Fundamental Research Funds for the Central Universities (Chongqing University, CDJZR10100009)National Science Foundation for Distinguished Young Scholars of China (11001226)
文摘Let G be a finite group and π（G） = {pl,p2,…… ,pk} be the set of the primes dividing the order of G. We define its prime graph F（G） as follows. The vertex set of this graph is 7r（G）, and two distinct vertices p, q are joined by an edge if and only if pq ∈ πe（G）. In this case, we write p - q. For p ∈π（G）, put deg（p） ：= ｜{q ∈ π（G）｜p - q}｜, which is called the degree of p. We also define D（G） ：= （deg（p1）, deg（p2）,..., deg（pk））, where pl 〈 p2 〈 -……〈 pk, which is called the degree pattern of G. We say a group G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and degree pattern as G. Specially, a l-fold OD-characterizable group is simply called an OD-characterizable group. Let L ：= U6（2）. In this article, we classify all finite groups with the same order and degree pattern as an almost simple groups related to L. In fact, we prove that L and L.2 are OD-characterizable, L.3 is 3-fold OD-characterizable, and L.S3 is 5-fold OD-characterizable.
