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RELATIVE ELEMENTARY ABELIAN GROUPS AND A CLASS OF EDGE-TRANSITIVE CAYLEY GRAPHS

Part of: Algebraic combinatorics Permutation groups Graph theory

Published online by Cambridge University Press:  20 November 2015

CAI HENG LI  and
LEI WANG
CAI HENG LI
Affiliation:
School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, PR China School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia email [email protected]
LEI WANG*
Affiliation:
School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, PR China email [email protected]
*
✉[email protected]
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Abstract

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Motivated by a problem of characterising a family of Cayley graphs, we study a class of finite groups $G$ which behave similarly to elementary abelian $p$-groups with $p$ prime, that is, there exists a subgroup $N$ such that all elements of $G\setminus N$ are conjugate or inverse-conjugate under $\mathsf{Aut}(G)$. It is shown that such groups correspond to complete multipartite graphs which are normal edge-transitive Cayley graphs.

Keywords

Cayley graphcomplete graphREA groupFrobenius group

MSC classification

Primary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 05E18: Group actions on combinatorial structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 100 , Issue 2 , April 2016 , pp. 241 - 251
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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