Characterising CCA Sylow cyclic groups whose order is not divisible by four

Authors

  • Luke Morgan The University of Western Australia, Australia
  • Joy Morris University of Lethbridge, Canada
  • Gabriel Verret The University of Western Australia, Australia

DOI:

https://doi.org/10.26493/1855-3974.1332.b49

Keywords:

CCA problem, Cayley graphs, edge-colouring, Sylow cyclic groups

Abstract

A Cayley graph on a group G has a natural edge-colouring. We say that such a graph is CCA if every automorphism of the graph that preserves this edge-colouring is an element of the normaliser of the regular representation of G. A group G is then said to be CCA if every connected Cayley graph on G is CCA.

Our main result is a characterisation of non-CCA graphs on groups that are Sylow cyclic and whose order is not divisible by four. We also provide several new constructions of non-CCA graphs.

Published

2017-05-09

Issue

Section

Articles