Semisymmetric cubic graphs as regular covers of K3,3

被引：66

作者：

Wang, Chang Qun ^{[1
]}

Chen, Tie Sheng ^{[1
]}

机构：

[1] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2008年 / 24卷 / 03期

基金：

中国国家自然科学基金;

关键词：

semisymmetric graph; symmetric graph; covering graph; one-regular graph;

D O I：

10.1007/s10114-007-0998-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A regular graph X is called semisymmetric if it is edge-transitive but not vertex-transitive. For G <= AutX, we call a G-cover X semisymmetric if X is semisymmetric, and call a G-cover X one-regular if AutX acts regularly on its arc-set. In this paper, we give the sufficient and necessary conditions for the existence of one-regular or semisymmetric Z(n)-covers of K-3,K-3. Also, an infinite family of semisymmetric Z(n) x Z(n)-covers of K-3,K-3 are constructed.

引用

页码：405 / 416

页数：12

共 22 条

[1]

Bouwer I. Z., 1972, Journal of Combinatorial Theory, Series B, V12, P32, DOI 10.1016/0095-8956(72)90030-5

[2]

BOUWER IZ, 1968, B CAN MATH SOC, V11, P533

[3]

Dixon JD., 1996, PERMUTATION GROUPS

[4] A classification of semisymmetric graphs of order 2pq [J].

Du, SF ;

Xu, MY .

COMMUNICATIONS IN ALGEBRA, 2000, 28 (06) :2685-2715

[5]

DU SF, 2000, UNPUB RES NOTES SEMI

[6]

DU SF, 1995, GRAPH THEORY NOTES N, V29, P148

[7] s-regular cubic graphs as coverings of the complete bipartite graph K3,3 [J].

Feng, YQ ;

Kwak, JH .

JOURNAL OF GRAPH THEORY, 2004, 45 (02) :101-112

[8]

Folkman J., 1967, J. Combinatorial Theory, V3, P215

[9] AUTOMORPHISMS OF TRIVALENT GRAPHS [J].

GOLDSCHMIDT, DM .

ANNALS OF MATHEMATICS, 1980, 111 (02) :377-406

[10]

Gorenstein D., 1980, Finite groups, V2

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