文献类型：期刊文献

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

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

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

第一作者：Songtao Guo

机构：[1]School of Mathematics and Statistics, Henan University of Science and Technology Luoyang, Henan 471023, China;[2]College of Arts and Science, Beijing Union University, Beijing 100091, China;[3]College of Mathematics and Information Science, Henan Normal University Xinxiang, Henan 453007, China

第一机构：School of Mathematics and Statistics, Henan University of Science and Technology Luoyang, Henan 471023, China

年份：2016

卷号：23

期号：3

起止页码：493-500

中文期刊名：代数集刊：英文版

外文期刊名：Algebra Colloquium

收录：Scopus;CSCD:【CSCD2015_2016】；

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 Re- search Foundation for Doctoral Scholars of HAUST （09001707）.

语种：中文

中文关键词：传递图;有限简单无向图;自同构群;同构判定;离散数学;稳定剂;顶点;立方图

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

摘要：让 X 是一张有限的简单的未受指导的图和 G X 的一个自守组。如果 G 在 s 弧上然而并非在上是及物的(s+1 ) 那么， X 被打电话给的弧(G， s ) 及物。让 X 一连接(G， s ) 主要原子价 p 的及物的图，和 G _v 在 G 的顶点 v V (X) 的顶点 stabilizer。为盒子 p=3， G _v 被 Djokovi 和米勒决定了在[立方的图的自守的常规组， J。Combin。理论(重量的单位。B ) 29 (1980 ) 195 - 230 ] 。为盒子 p=5， G _v 被郭和冯给了在里面[五价的 s 及物的图上的笔记，分离 Math.312 (2012 ) 2214 - 2216 ] 。在这份报纸，我们处理盒子 p=7 并且决定顶点 stabilizer G _v 。
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 Gv the vertex stabilizer of a vertex v E V（X） in G. For the case p = 3, the exact structure of Gv has been determined by Djokovid 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 Gv 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 Gv.