Year: 2025
Type: article
Abstract: A set of vertices of a graph is distinguishing if the only automorphism that preserves it is the identity. The minimal size of such sets, if they exist, is the distinguishing cost. The distinguishing costs ofvertex transitive cubic graphs are well known if they are 1-arc-transitive, or if they have two edge orbits and either have girth 3 or vertex-stabilizers of order 1 or 2. There are many results about vertex-transitive cubic graphs of girth 4 with two edge orbits, but for larger girth almost nothing is known about the distinguishing costs of such graphs.We prove that cubic vertex-transitive graphs of girth 5 with two edge orbits have distinguishing cost 2, and prove the non-existence of infinite 3-arc-transitive cubic graphs of girth 6.
Institutions: University of Primorska, Montanuniversität Leoben
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: OeAD-GmbH
OpenAlex ID: W4413306553