Some results on the lexicographic product of vertex-transitive graphs

被引：37

作者：

Li, Feng ^{[1
]}

Wang, Wei ^{[1
]}

Xu, Zongben ^{[1
]}

Zhao, Haixing ^{[2
]}

机构：

[1] Xi An Jiao Tong Univ, Fac Sci, Inst Informat & Syst Sci, Xian 710049, Peoples R China

[2] Qinghai Normal Univ, Dept Math, Xining 810003, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2011年 / 24卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Cayley graph; Lexicographic product; Vertex-transitive graph;

D O I：

10.1016/j.aml.2011.05.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Many large graphs can be constructed from existing smaller graphs by using graph operations, for example, the Cartesian product and the lexicographic product. Many properties of such large graphs are closely related to those of the corresponding smaller ones. In this short note, we give some properties of the lexicographic products of vertex-transitive and of edge-transitive graphs. In particular, we show that the lexicographic product of Cayley graphs is a Cayley graph. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1924 / 1926

页数：3

共 13 条

[1] A CONSTRUCTION FOR VERTEX-TRANSITIVE GRAPHS [J].

ALSPACH, B ;

PARSONS, TD .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1982, 34 (02) :307-318

[2]

Bondy J. A., 1976, Graduate Texts in Mathematics, V290

[3]

BROERE I, 1990, QUAEST MATH, V13, P191

[4]

FEDER T, 1995, MEM AM MATH SOC, V116, P1

[5] On normal Cayley graphs and hom-idempotent graphs [J].

Larose, B ;

Laviolette, F ;

Tardif, C .

EUROPEAN JOURNAL OF COMBINATORICS, 1998, 19 (07) :867-881

[6] WHICH GENERALIZED PETERSEN GRAPHS ARE CAYLEY-GRAPHS [J].

NEDELA, R ;

SKOVIERA, M .

JOURNAL OF GRAPH THEORY, 1995, 19 (01) :1-11

[7]

NGO DT, 1996, DISCRETE MATH, V151, P231

[8] Mobility of vertex-transitive graphs [J].

Potocnik, Primoz ;

Sajna, Mateja ;

Verret, Gabriel .

DISCRETE MATHEMATICS, 2007, 307 (3-5) :579-591

[9]

Sabidussi G., 1968, MONATSH MATH, V68, P426

[10]

Sanders R. S., 1997, Journal of Combinatorial Mathematics and Combinatorial Computing, V24, P119

← 1 2 →