Finite normal edge-transitive Cayley graphs
Finite normal edge-transitive Cayley graphs
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DOI：
10.1017/s0004972700036340
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发表时间：
1999-10
影响因子：
0.7
通讯作者：
C. Praeger
中科院分区：
文献类型：
--
作者：
C. Praeger
本文给出了有限群G的Cayley图族的一种分析方法，它将正规边传递Cayley图族确定为中心重要性的一个子族。这些都是凯莱图G的一个子群的自同构存在的规范G和行为传递的边缘。证明了对一个非平凡群G，G的每个正规边传递Cayley图至少有一个同态象是G的特征单商群的正规边传递Cayley图.此外，给出了商群G/H的正规边传递Cayley图ΓH，得到了G存在正规边传递Cayley图的充要条件，并给出了求这类图的方法.
An approach to analysing the family of Cayley graphs for a finite group G is given which identifies normal edge-transitive Cayley graphs as a sub-family of central importance. These are the Cayley graphs for G for which a subgroup of automorphisms exists which both normalises G and acts transitively on edges. It is shown that, for a nontrivial group G, each normal edge-transitive Cayley graph for G has at least one homomorphic image which is a normal edge-transitive Cayley graph for a characteristically simple quotient group of G. Moreover, given a normal edge-transitive Cayley graph ΓH for a quotient group G/H, necessary and sufficient conditions are obtained for the existence of a normal edge-transitive Cayley graph Γ for G which has ΓH as a homomorphic image, and a method for obtaining all such graphs Γ is given.