Cubic Edge-Transitive bi-Cayley Graphs on Generalized Dihedral Group

被引：1

作者：

Wang, Xue ^{[1
]}

机构：

[1] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2022年 / 45卷 / 01期

关键词：

Edge-transitive; Bi-Cayley graph; Girth; Generalized dihedral group;

D O I：

10.1007/s40840-021-01205-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we first prove that the connected cubic edge-transitive bi-Cayley graphs over a generalized dihedral group have girth 6. Using this, a complete classification is given of these graphs.

引用

页码：537 / 547

页数：11

共 13 条

[1] The Magma algebra system .1. The user language [J].

Bosma, W ;

Cannon, J ;

Playoust, C .

JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) :235-265

[2]

Conder M., 2002, J COMB MATH COMB COM, V40, P41

[3] Symmetric cubic graphs of small girth [J].

Conder, Marston ;

Nedela, Roman .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2007, 97 (05) :757-768

[4] Edge-transitive bi-Cayley graphs [J].

Conder, Marston ;

Zhou, Jin-Xin ;

Feng, Yan-Quan ;

Zhang, Mi-Mi .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2020, 145 :264-306

[5] Characterization of edge-transitive 4-valent bicirculants [J].

Kovacs, Istvan ;

Kuzman, Bostjan ;

Malnic, Aleksander ;

Wilson, Steve .

JOURNAL OF GRAPH THEORY, 2012, 69 (04) :441-463

[6]

Marusic D, 2000, CROAT CHEM ACTA, V73, P969

[7] A classification of cubic bicirculants [J].

Pisanski, Tomaz .

DISCRETE MATHEMATICS, 2007, 307 (3-5) :567-578

[8]

Suzuki M., 1982, Group Theory I, V247

[9] Trivalent dihedrants and bi-dihedrants [J].

Zhang, Mi-Mi ;

Zhou, Jin-Xin .

ARS MATHEMATICA CONTEMPORANEA, 2021, 21 (02)

[10] Trivalent vertex-transitive bi-dihedrants [J].

Zhang, Mi-Mi ;

Zhou, Jin-Xin .

DISCRETE MATHEMATICS, 2017, 340 (08) :1757-1772

← 1 2 →