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## 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.

Original language | English |
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Pages (from-to) | 173-187 |

Number of pages | 15 |

Journal | Ars Mathematica Contemporanea |

Volume | 19 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 2020 |

## Keywords

- Distinguishing number
- Symmetry breaking in graph
- Vertex colouring
- Vertex-transitive graphs

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Algebra and Number Theory

## Fields of Expertise

- Information, Communication & Computing

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Dive into the research topics of 'Distinguishing numbers of finite 4-valent vertex-transitive graphs'. Together they form a unique fingerprint.## Projects

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