Abstract:
© 2020 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved. 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.