On Cayley Graphs of Abelian Groups

Authors:
Cai Heng Li
Affiliations:
Department of Mathematics, University of Western Australia, Nedlands, W.A. 6907, Australia. E-mail: li@maths.uwa.edu.au
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
1998

Citing 6
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Abstract

Let G be a finite Abelian group and Cay(G,S) the Cayley (di)-graph of G with respectto S, and let A = Aut Cay(G,S) and A_1 the stabilizer of 1 in A. In thispaper, we first prove that if A_1 is unfaithful onS then S contains a coset of some nontrivialsubgroup of G, and then characterize Cay(G,S) ifA_1^S contains the alternating group on S.Finally, we precisely determine all m-DCIp-groups for 2 ≤ m ≤ p + 1, where p isa prime.