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 of vertex 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.

Rights

URN

URN:NBN:SI:DOC-9WJIPCPJ

COBISSID

246737923

DOI

10.26493/2590-9770.1724.18a

Added

20.02.2026

Metadata

Citation

APA:

Dobson, Edward Tauscher, Hujdurović, Ademir, Imrich, Wilfried, Ortner, Ronald (2025). On cubic vertex-transitive graphs of given girth. The art of discrete and applied mathematics, volume 8, issue 1, article p1.12, str. 1-16. URN:NBN:SI:DOC-9WJIPCPJ from http://www.dlib.si

MLA:

Dobson, Edward Tauscher, Hujdurović, Ademir, Imrich, Wilfried, Ortner, Ronald. "On cubic vertex-transitive graphs of given girth." The art of discrete and applied mathematics volume 8. issue 1. article p1.12 (2025) str. 1-16.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-9WJIPCPJ>