共查询到19条相似文献,搜索用时 234 毫秒
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关于半传递图的若干新结果 总被引:1,自引:0,他引:1
我们称无向图X为半传递的,如果它的自同构群Aut X在X的顶点集合以及边集合上作用是传递的,但在X的有序的相邻顶点对的集合上作用非传递。本文综述了自1990年以来若干数学家包括作者本人在半传递图方面研究的最新结果,特别地,我们的工到了具有本原自同构群的半传递图,从而肯定地回答了Holton问题,同时还证明了只存在一个4度27阶的半传递图,解决了Holt问题。 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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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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图X是一个有限简单无向图,如果图X是正则的且边传递但非点传递,则称X是半对称图.主要利用仿射几何构造了一类2p~n阶连通p~4度的半对称图的无限族,其中p≥n≥11. 相似文献
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王丽 《数学的实践与认识》2012,42(1):234-241
称一个有限简单无向图X是半对称图,如果图X是正则的且边传递但非点传递.主要利用仿射几何构造了一类2p~n阶连通p~3。度的半对称图的无限族,其中p≥n≥8. 相似文献
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王丽 《数学的实践与认识》2011,41(10)
称一个有限简单无向图X是半对称图,如果图X是正则的且边传递但非点传递.本文主要利用仿射几何构造了一类2p~n阶连通p~2度的半对称图的无限族,其中p≥n≥5. 相似文献
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肖仁兵邓伟升 《数学的实践与认识》2022,(9):180-187
一个图Γ称之为边本原图.若Γ的全自同构群作用在Γ的边集上是本原的.边本原图是一类重要的对称图,这类图不是很多,但一些著名的图,比如Heawood图,Tutte-Coxeter图和Higman-Sims图都是边本原图.我们通过构造陪集图的方法来研究边本原图,并给出了基柱为Mathieu群的几乎单群上边本原图的分类. 相似文献
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A regular and edge-transitive graph which is not vertex-transitive is said to be semisymmetric. Every semisymmetric graph is necessarily bipartite, with the two parts having equal size and the automorphism group acting transitively on each of these parts. A semisymmetric graph is called biprimitive if its automorphism group acts primitively on each part. In this paper biprimitive graphs of smallest order are determined. 相似文献
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A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. This paper gives a classification of semisymmetric graphs of order 2pq where p and q are distinct primes. It is shown that there are 143 examples of such graphs, 131 of which are biprimitive. 相似文献
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二面体群D_(2n)的4度正规Cayley图 总被引:4,自引:0,他引:4
设G是有限群,S是G的不包含单位元1的非空子集.定义群G关于S的 Cayley(有向)图X=Cay(G,S)如下:V(x)=G,E(X)={(g,sg)|g∈G,s∈S}. Cayley图X=Cay(G,S)称为正规的如果R(G)在它的全自同构群中正规.图X称为1-正则的如果它的全自同构群在它的弧集上正则作用.本文对二面体群D2n以Z22 为点稳定子的4度正规Cayley图进行了分类. 相似文献
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图X称为边正则图,若X的自同构群Aut(X)在X的边集上的作用是正则的.本文考察了三度边正则图与四度Cayley图的关系,给出了一个由四度Cayley图构造三度边正则图的方法,并且构造了边正则图的三个无限族. 相似文献
15.
An undirected graph without isolated vertices is said to be semisymmetric if its full automorphism group acts transitively
on its edge set but not on its vertex set. In this paper, we inquire the existence of connected semisymmetric cubic graphs
of order 16p
2. It is shown that for every odd prime p, there exists a semisymmetric cubic graph of order 16p
2 and its structure is explicitly specified by giving the corresponding voltage rules generating the covering projections. 相似文献
16.
Classifying cubic symmetric graphs of order 10p or 10p~2 总被引:1,自引:0,他引:1
KWAK Jin Ho 《中国科学A辑(英文版)》2006,49(3)
A graph is called s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, the s-regular cyclic or elementary abelian coverings of the Petersen graph for each s ≥ 1 are classified when the fibre-preserving automorphism groups act arc-transitively. As an application of these results, all s-regular cubic graphs of order 10p or 10p2 are also classified for each s ≥ 1 and each prime p, of which the proof depends on the classification of finite simple groups. 相似文献
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Let be a regular covering projection of connected graphs with the group of covering transformations isomorphic to N. If N is an elementary abelian p-group, then the projection ℘N is called p-elementary abelian. The projection ℘N is vertex-transitive (edge-transitive) if some vertex-transitive (edge-transitive) subgroup of the automorphism group of X lifts along ℘N, and semisymmetric if it is edge- but not vertex-transitive. The projection ℘N is minimal semisymmetric if it cannot be written as a composition ℘N=℘℘M of two (nontrivial) regular covering projections, where ℘M is semisymmetric.Malni? et al. [Semisymmetric elementary abelian covers of the Möbius-Kantor graph, Discrete Math. 307 (2007) 2156-2175] determined all pairwise nonisomorphic minimal semisymmetric elementary abelian regular covering projections of the Möbius-Kantor graph, the Generalized Petersen graph GP(8,3), by explicitly giving the corresponding voltage rules generating the covering projections. It was remarked at the end of the above paper that the covering graphs arising from these covering projections need not themselves be semisymmetric (a graph with regular valency is said to be semisymmetric if its automorphism group is edge- but not vertex-transitive). In this paper it is shown that all these covering graphs are indeed semisymmetric. 相似文献
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A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify hexavalent symmetric graphs of order for each prime . 相似文献
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Jin‐Xin Zhou 《Journal of Graph Theory》2012,71(4):402-415
A graph is vertex‐transitive if its automorphism group acts transitively on vertices of the graph. A vertex‐transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this article, the tetravalent vertex‐transitive non‐Cayley graphs of order 4p are classified for each prime p. As a result, there are one sporadic and five infinite families of such graphs, of which the sporadic one has order 20, and one infinite family exists for every prime p>3, two families exist if and only if p≡1 (mod 8) and the other two families exist if and only if p≡1 (mod 4). For each family there is a unique graph for a given order. © 2011 Wiley Periodicals, Inc. 相似文献