文献类型：期刊文献

英文题名：(G, s)-Transitive Graphs of Valency 7

作者：Guo, Songtao[1];Li, Yantao[2];Hua, Xiaohui[3]

第一作者：Guo, Songtao

通讯作者：Guo, ST[1]

机构：[1]Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Henan, Peoples R China;[2]Beijing Union Univ, Coll Arts & Sci, Beijing 100091, Peoples R China;[3]Henan Normal Univ, Coll Mat & Informat Sci, Xinxiang 453007, Henan, Peoples R China

第一机构：Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Henan, Peoples R China

通讯机构：[1]corresponding author), Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Henan, Peoples R China.

年份：2016

卷号：23

期号：3

起止页码：493-500

外文期刊名：ALGEBRA COLLOQUIUM

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000382581800011)】；

基金：This work was supported by the National Natural Science Foundation of China (11301154, 11271012, 11301159, 11101035, 11326056), the Key Project of Education Department of Henan Province Scientific and Technological Research (13A110249) and the Scientific Research Foundation for Doctoral Scholars of HAUST (09001707).

语种：英文

外文关键词：symmetric graph; s-transitive graph; (G, s)-transitive graph

摘要：Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on (s+1)-arcs then X is called (G,s)-transitive. Let X be a connected (G,s)-transitive graph of a prime valency p, and G(v) the vertex stabilizer of a vertex v is an element of V(X) in G. For the case p=3, the exact structure of G(v) has been determined by Djokovic and Miller in [Regular groups of automorphisms of cubic graphs, J. Combin. Theory (Ser. B) 29 (1980) 195 - 230]. For the case p=5, all the possibilities of G(v) have been given by Guo and Feng in [A note on pentavalent s-transitive graphs, Discrete Math.312 (2012) 2214 - 2216]. In this paper, we deal with the case p=7 and determine the exact structure of the vertex stabilizer G(v).