On colour-preserving automorphisms of Cayley graphs
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
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