A characterization of tetravalent half-arc-transitive graphs of girth 5
Abstract
A graph is said to be half-arc-transitive if its automorphism group is transitive on the vertices and the edges of the graph but not on its arcs. Tetravalent half-arc-transitive graphs of girth 3 were characterized by Marušič and Xu in 1997, while those of girth 4 were characterized by Marušič and Nedela in 2002 and by Potočnik and Wilson in 2007. The investigation of tetravalent half-arc-transitive graphs of girth 5 was initiated by Antončič and Šparl in 2023. In this paper, a characterization of all tetravalent half-arc-transitive graphs of girth 5 is given, and as an application, two open questions from Antončič and Šparl (2023) [1] are answered.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Graph Theory Research
Graph theory and applications
Publication details
- Journal / source
- Journal of Combinatorial Theory Series A
- Volume
- 221
- Pages
- 106167–106167
- Publication date
- 29 January 2026
- Language
- EN