共查询到15条相似文献,搜索用时 62 毫秒
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如果图X的全自同构群Aut(X)作用在其顶点集V(X)和边集E(X)上都是传递的,但作用在弧集Arc(X)上非传递,则称X是半传递图.研究了4p~2(p3且p≡-1(mod4))阶4度半传递图,确定了4p~2阶4度半传递图的连通性及其自同构群的阶. 相似文献
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李学文 《数学的实践与认识》2005,35(8):233-238
群G关于S的有向Cayley图X=Cay(G,S)称为pk阶有向循环图,若G是pk阶循环群.利用有限群论和图论的较深刻的结果,对p2阶弧传递(有向)循环图的正规性条件进行了讨论,证明了任一p2阶弧传递(有向)循环图是正规的当且仅当(|Aut(G,S)|,p)=1. 相似文献
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如果一个图Γ含有一个自同构群G使得它在顶点集V(Γ)上作用半正则且恰好有两个轨道,则称图r是群G上的双凯莱图.进一步的,如果G在全自同构群Aut(Γ)中正规,我们就称这个双凯莱图是群G上的正规双凯莱图.本文中,我们证明了绝大多数非交换单群G上的三度点传递双凯莱图都是该群上的正规双凯莱图. 相似文献
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图Γ称为点传递自补图,如果Γ的图自同构群AutΓ在顶点集合VΓ作用是传递的,且Γ的补图(Γ)与图Γ是同构的.本文主要研究了通过Cayley同构来构造点自补Cayley图,并证明了内循环群上的这类图必然是循环自补图. 相似文献
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主要给出几类非交换群对Alspach猜想(当Cay(G,S)的度小于等于4时)成立,进一步对2n和2p2阶群Cayley图的Hamilton圈的分解进行了讨论. 相似文献
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成会文 《数学的实践与认识》2011,41(4)
群G的Cayley图Cay(G,S)称为是正规的,如果G的右正则表示R(G)在Cay(G,S)的全自同构群中正规.设p为奇素数,相关文献决定了4p阶连通3度Cayley图的正规性.本文给出了上述文献的主要结果的一个新的简短的证明. 相似文献
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A graph X is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut (X) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call X a semisymmetric graph. Let p be a prime. It was shown by Folkman (J Comb Theory 3:215–232, 1967) that a regular edge-transitive graph of order 2p or 2p 2 is necessarily vertex-transitive. The smallest semisymmetric graph is the Folkman graph. In this study, we classify all connected cubic semisymmetric graphs of order 18p n , where p is a prime and \({n \geq 1}\) . 相似文献
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Acta Mathematicae Applicatae Sinica, English Series - A regular edge-transitive graph is said to be semisymmetric if it is not vertex-transitive. Let p be a prime. By Folkman [J. Combin. Theory 3... 相似文献
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We investigate the family of vertex-transitive graphs with diameter 2. Let Γ be such a graph.Suppose that its automorphism group is transitive on the set of ordered non-adjacent vertex pairs. Then either Γ is distance-transitive or Γ has girth at most 4. Moreover, if Γ has valency 2, then Γ≌ C4 or C5; and for any integer n ≥ 3, there exist such graphs Γ of valency n such that its automorphism group is not transitive on the set of arcs. Also, we determine this family of grap... 相似文献
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Let s be a positive integer. A graph is s -transitive if its automorphism group is transitive on s-arcs but not on (s?+?1)-arcs. Let p be a prime. Zhou (Discrete Math 309:6081?C6086, 2009) classified tetravalent s-transitive graphs of order 4p. In this article a complete classification of tetravalent s-transitive graphs of order 4p 2 is given. 相似文献