Geodesic
Distinguishing numbers of finite 4-valent vertex-transitive graphs
Ars Mathematica Contemporanea, Tome 19 (2020) no. 2, pp. 173-187.

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The distinguishing number of a graph G is the smallest k such that G admits a k-colouring for which the only colour-preserving automorphism of G is the identity. We determine the distinguishing number of finite 4-valent vertex-transitive graphs. We show that, apart from one infinite family and finitely many examples, they all have distinguishing number 2.
DOI : 10.26493/1855-3974.1849.148
Keywords: Vertex colouring, symmetry breaking in graph, distinguishing number, vertex-transitive graphs 
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Florian Lehner; Gabriel Verret. Distinguishing numbers of finite 4-valent vertex-transitive graphs. Ars Mathematica Contemporanea, Tome 19 (2020) no. 2, pp. 173-187. doi : 10.26493/1855-3974.1849.148. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1849.148/

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