Distinguishing numbers of finite $4$-valent vertex-transitive graphs

Florian Lehner; Gabriel Verret

Distinguishing numbers of finite $4$-valent vertex-transitive graphs

Combinatorics 2020-02-24 v2

Authors: Florian Lehner , Gabriel Verret

Abstract

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 $2$ .

Keywords

distinguishing number 4-valent graphs vertex-transitive graphs graph colouring automorphism

Cite

@article{arxiv.1810.01522,
  title  = {Distinguishing numbers of finite $4$-valent vertex-transitive graphs},
  author = {Florian Lehner and Gabriel Verret},
  journal= {arXiv preprint arXiv:1810.01522},
  year   = {2020}
}

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