Weakly s-arc transitive graphs

被引：0

作者：

Yan, Hongming ^{[2
]}

Fan, Suohai ^{[1
]}

机构：

[1] Jinan Univ, Dept Math, Guangzhou 510632, Peoples R China

[2] Zhongkai Agrotech Coll, Dept Math, Guangzhou 510225, Peoples R China

来源：

DISCRETE MATHEMATICS | 2008年 / 308卷 / 12期

基金：

中国国家自然科学基金;

关键词：

weakly s-arc transitive; endomorphism; girth; retract; core;

D O I：

10.1016/j.disc.2007.06.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Weakly s-arc transitive graphs are introduced and determined. A graph is said to be weakly s-arc transitive if its endomorphism monoid acts transitively on the set of s-arcs. The main results are: (1) A nonbipartite graph is weakly s-arc transitive if and only if it is s-arc transitive. (2) A tree with diameter d is weakly s-arc transitive for all 0 <= s <= d. (3) A bipartite graph with girth g = 2s is always weakly t-arc transitive for all 0 <= t <= s, but not weakly (s + 2)-arc transitive. Further, a bipartite graph with girth g = 2s is weakly (s + 1)-arc transitive if and only if the graph has diameters. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：2643 / 2646

页数：4

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