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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Lehner Smith - On symmetries of edge and vertex colourings of graphs - DM Accepted version.pdf - Whole Document Restricted to Repository staff only until 22 May 2021. 358kB |
Item Type: | Article |
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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 |
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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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