摘要
我们称无向图X为半传递的,如果它的自同构群AutX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,我们找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。
We call an undirected graph X 1/2-transitive,if the automorphism group Aut X of X acts transitively on the vertex set and edge set,but not on the set of ordered pairs of adjacent vertices of X.In this paper we survey some new results on 1/2-transitive graphs which have been obtained since 1990 by the author and some other researchers.In particular,the Holton’s question was affirmatively answered by finding some examples of 1/2-transitive graphs with primitive automorphism groups, and the Holt’s questions were also answered by proving that the smallest 1/2-transitive graph has 27 vertices and that there is only one such graph of degree 4.
出处
《数学进展》
CSCD
北大核心
1994年第6期505-516,共12页
Advances in Mathematics(China)