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AUTOMORPHISM GROUPS OF SELF-COMPLEMENTARY VERTEX-TRANSITIVE GRAPHS

Part of: Graph theory Permutation groups

Published online by Cambridge University Press:  11 November 2015

ZHAOHONG HUANG ,
JIANGMIN PAN ,
SUYUN DING  and
ZHE LIU
ZHAOHONG HUANG
Affiliation:
School of Mathematics and Statistics, Yunnan University, Kunming, PR China
JIANGMIN PAN*
Affiliation:
School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, PR China email jmpan@ynu.edu.cn
SUYUN DING
Affiliation:
School of Mathematics and Statistics, Yunnan University, Kunming, PR China
ZHE LIU
Affiliation:
College of Science, Zhejiang University of Agriculture and Forestry, Hangzhou, PR China
*
✉jmpan@ynu.edu.cn
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Abstract

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Li et al. [‘On finite self-complementary metacirculants’, J. Algebraic Combin.40 (2014), 1135–1144] proved that the automorphism group of a self-complementary metacirculant is either soluble or has $\text{A}_{5}$ as the only insoluble composition factor, and gave a construction of such graphs with insoluble automorphism groups (which are the first examples of self-complementary graphs with this property). In this paper, we will prove that each simple group is a subgroup (so is a section) of the automorphism groups of infinitely many self-complementary vertex-transitive graphs. The proof involves a construction of such graphs. We will also determine all simple sections of the automorphism groups of self-complementary vertex-transitive graphs of $4$-power-free order.

Keywords

self-complementary graphautomorphism groupsimple section

MSC classification

Primary: 20B15: Primitive groups
Secondary: 20B30: Symmetric groups 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 2 , April 2016 , pp. 238 - 247
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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