2p2阶3度Cayley图

Cayley图Cay(G,S)称之为正规的,如果G的右正则表示是Cay(G,S)全自同构群的正规子群。本文决定了2p~2(p为素数)阶群上3度连通Cayley图的正规性,作为该结果的一个应用,对每一个1(?)s(?)5,对2p~2阶3度s-正则Cayley图作了分类。     

Petersen图的点传递正则覆盖图

运用基图自同构能被提升的线性准则 ,对满足 :1覆叠变换群 K =Znp,2覆盖图的保簇变换群是点传递的 Petersen图的连通正则覆盖图进行了完全分类 .这种图共有 1 2种类型 .     

4p阶3度点传递图

一个图称为点传递图,如果它的全自同构群在它的顶点集合上作用传递.证明了一个4p(p为素数)阶连通3度点传递图或者是Cayley图,或者同构于下列之一;广义Petersen图P(10,2),正十二面体,Coxeter图,或广义Petersen图P(2p,k),这里k2≡-1(mod 2p).     

Automorphism Group of the Rank-decreasing Graph Over the Semigroup of Upper Triangular Matrices

Let F_q be a finite field with q elements, n ≥ 2 a positive integer, and T(n, q) the semigroup of all n × n upper triangular matrices over F_q. The rank-decreasing graph 𝕋 of T(n, q) is a directed graph which has T(n, q) as vertex set, and there is a directed edge from A ∈ T(n, q) to B ∈ T(n, q) if and only if r(AB) < r(B). The zero-divisor graph 𝒯 of T(n, q), with vertex set of all nonzero zero-divisors of T(n, q) and there is a directed edge from a vertex A to a vertex B if and only if AB = 0, can be viewed as a subgraph of 𝕋. In [16 Wang, L. (2015). A note on automorphisms of the zero-divisor graph of upper triangular matrices. Lin. Alg. Appl. 465:214–220.[Crossref], [Web of Science ®] , [Google Scholar]], L. Wang has determined the automorphisms of the zero-divisor graph 𝒯 of T(n, q). In this article, by applying the main result of [17 Wong, D., Ma, X., Zhou, J. (2014). The group of automorphisms of a zero-divisor graph based on rank one upper triangular matrices. Lin. Alg. Appl. 460:242–258.[Crossref], [Web of Science ®] , [Google Scholar]] we determine the automorphisms of the rank-decreasing graph 𝕋 of T(n, q).     

对称群上Cayley图的条件匹配排除数

一个图的条件匹配排除数是最少的边的数量,使得从图中删除这些边后形成的图既没有孤立点,也没有完美匹配和几乎完美匹配.条件匹配排除数是衡量网络在边故障情况下的鲁棒性的参数之一.本文给出了对称群上Cayley图的条件匹配排除数.     

On non-normal arc-transitive 4-valent dihedrants

Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group Dn such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within Dn. It is shown that X is isomorphic either to the lexicographic product Cn[2K1] with n 〉 4 even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively.     

具有4pq阶自同构群的有限群

本文讨论了自同构群阶为4pq(p,q为不同奇素数)的有限群,得出了它们的构造.     

On the Automorphism Group of a Semifield of Order 54

The purpose of this article is to determine Aut(A) where A is a semifield of order 5⁴ admitting an automorphism group E ? Z ₂ × Z ₂ acting freely on A.     

On the Maximum Matching Graph of a Graph

1IntroductionMatchingtheory,aswellastheassignmentprobleminlinearprogramming,hasawiderangeofapplicationinthetheoryandpracticeofoperationsresearch.Bysomepracticalmotivations,e.g.,forfindingalloptimalsolutions,peoplewanttoknowthestructurepropertiesofallmaximummatchingsofagraphG.InthecasethatGhasperfectmatchings,extensiveworkhasbeendoneontheso-calledperfectmatChinggrape(or1-factorgraph),inwhichtwoperfectmatchingsMIandMZaresaidtobeadjacentifMI~MZ@E(C)whereCisanMI-alternatingcycleofG.Therewer…