On colour-preserving automorphisms of Cayley graphs

Authors

  • Ademir Hujdurović University of Primorska
  • Klavdija Kutnar University of Primorska
  • Dave Witte Morris University of Lethbridge
  • Joy Morris University of Lethbridge

DOI:

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

Keywords:

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

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.

Published

2015-10-20

Issue

Section

Articles