On colour-preserving automorphisms of Cayley graphs

Ademir Hujdurović, Klavdija Kutnar, Dave Witte Morris, Joy Morris

Abstract


We study the automorphisms of a Cayley graph that preserve its natural edge-colouring. More precisely, we are interested in groups G, such that every such automorphism of every connected Cayley graph on G has a very simple form: the composition of a left-translation and a group automorphism. We find classes of groups that have the property, and we determine the orders of all groups that do not have the property. We also have analogous results for automorphisms that permute the colours, rather than preserving them.

Keywords


Cayley graph, automorphism, colour-preserving, colour-permuting

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DOI: https://doi.org/10.26493/1855-3974.771.9b3

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications