# Monika Pilśniak: Proper distinguishing arc-colourings of symmetric digraphs

Date of publication: 1. 4. 2022

Discrete mathematics seminar

Tuesday

5

April

Time:

10:15

Location:

Plemljev seminar, Jadranska 19

A symmetric digraph G' arises from a simple graph G by substituting each edge uv by a pair of opposite arcs uv, vu. An arc-colouring c of G' is distinguishing if the only automorphism of G' preserving c is the identity. We study distinct types of proper arc-colourings of G' corresponding to four definitions of adjacency of arcs. For each type, we investigate the distinguishing chromatic index of G', i.e. the least number of colours in a distinguishing proper colouring of G'. We also determine tight bounds for chromatic indices of G', i.e. for the least numbers of colours in each type of proper colourings.