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RELATIVE ELEMENTARY ABELIAN GROUPS AND A CLASS OF EDGE-TRANSITIVE CAYLEY GRAPHS
Part of
CAI HENG LI, LEI WANG
Journal:

Journal of the Australian Mathematical Society / Volume 100 / Issue 2 / April 2016

Published online by Cambridge University Press:

20 November 2015, pp. 241-251

Print publication:

April 2016
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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.