Distinguishing arc-colourings of symmetric digraphs
DOI:
https://doi.org/10.26493/2590-9770.1472.24bKeywords:
Symmetry breaking, distinguishing index, distinguishing chromatic indexAbstract
A symmetric digraph is obtained from an undirected graph
by replacing each edge uv of
by a pair of opposite arcs
and
. An arc-colouring of a digraph is called distinguishing if the only automorphism preserving it is the identity. The least number of colours in a distinguishing arc-colouring, not necessarily proper, of
is called the distinguishing index D'(
). We study bounds for D'(
). For proper distinguishing arc-colourings, the least number of colours is called the distinguishing chromatic index of
. There are 15 possible types of proper arc-colourings of a digraph depending on the definition of adjacent arcs. In this paper we investigate distinguishing chromatic indices of
for the nine remaining types not considered in our two previous papers. We formulate several conjectures.
