Lehner, Florian and Smith, Simon M (2020) On symmetries of edge and vertex colourings of graphs. Discrete Mathematics, 343 (9). p. 111959. ISSN 0012365X
Full content URL: https://doi.org/10.1016/j.disc.2020.111959
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Lehner Smith  On symmetries of edge and vertex colourings of graphs  DM Accepted version.pdf  Whole Document 358kB 
Item Type:  Article 

Item Status:  Live Archive 
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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