Two new families of non-CCA groups

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Date
2021
Authors
Fuller, Brandon
Morris, Joy
Journal Title
Journal ISSN
Volume Title
Publisher
University of Primorska
The Slovenian Discrete and Applied Mathematics Society
Abstract
We determine two new infinite families of Cayley graphs that admit colour-preserving automorphisms that do not come from the group action. By definition, this means that these Cayley graphs fail to have the CCA (Cayley Colour Automorphism) property, and the corresponding infinite families of groups also fail to have the CCA property. The families of groups consist of the direct product of any dihedral group of order 2n where n ≥ 3 is odd, with either itself, or the cyclic group of order n. In particular, this family of examples includes the smallest non-CCA group that does not fit into any previous family of known non-CCA groups.
Description
Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
Keywords
Cayley graphs , Automorphisms , Colour preserving , CCA
Citation
Fuller, B., & Morris, J. (2021). Two new families of non-CCA groups. The Art of Discrete and Applied Mathematics, 4, Article #P1.08. https://doi.org/10.26493/2590-9770.1370.445
URI
https://hdl.handle.net/10133/7258
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Morris, Joy