(G, s)-Transitive Graphs of Valency 7

被引：32

作者：

Guo, Songtao ^{[1
]}

Li, Yantao ^{[2
]}

Hua, Xiaohui ^{[3
]}

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

来源：

ALGEBRA COLLOQUIUM | 2016年 / 23卷 / 03期

基金：

中国国家自然科学基金;

关键词：

symmetric graph; s-transitive graph; (G; s)-transitive graph; S-TRANSITIVE GRAPHS; PROJECTIVE SUBORBITS; ARC TRANSITIVITY; ORDER;

D O I：

10.1142/S100538671600047X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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).

引用

页码：493 / 500

页数：8