Cayley graphs of more than one abelian group
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Date
2021
Authors
Dobson, Edward
Morris, Joy
Journal Title
Journal ISSN
Volume Title
Publisher
University of Primorska
Abstract
We show that for certain integers n, the problem of whether or not a Cayley digraph Γ of ℤn is also isomorphic to a Cayley digraph of some other abelian group G of order n reduces to the question of whether or not a natural subgroup of the full automorphism group contains more than one regular abelian group up to isomorphism (as opposed to the full automorphism group). A necessary and sufficient condition is then given for such circulants to be isomorphic to Cayley digraphs of more than one abelian group, and an easy-to-check necessary condition is provided.
Description
Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
Keywords
Cayley graph , Circulant graph , Group
Citation
Dobson, E., & Morris, J. (2021). Cayley graphs of more than one abelian group. The Art of Discrete and Applied Mathematics, 4(3), Article #P3.11. https://doi.org/10.26493/2590-9770.1352.4dc