On symmetries of edge and vertex colourings of graphs

Lehner, Florian and Smith, Simon M (2020) On symmetries of edge and vertex colourings of graphs. Discrete Mathematics, 343 (9). p. 111959. ISSN 0012-365X

Full content URL: https://doi.org/10.1016/j.disc.2020.111959

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On symmetries of edge and vertex colourings of graphs
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Abstract

Let c and c' be edge or vertex colourings of a graph G. The stabiliser of c is the set of automorphisms of G that preserve the colouring.
We say that c' is less symmetric than c if the stabiliser of c' is contained in the stabiliser of c.

We show that if G is not a bicentred tree, then for every vertex colouring of G there is a less symmetric edge colouring with the same number of colours. On the other hand, if T is a tree, then for every edge colouring there is a less symmetric vertex colouring with the same number of colours.

Our results can be used to characterise those graphs whose distinguishing index is larger than their distinguishing number.

Keywords:Distinguishing number, symmetry breaking
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:40542
Deposited On:09 Apr 2020 11:14

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