Work

A characterization of tetravalent half-arc-transitive graphs of girth 5

Year: 2026

Type: article

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.

Source: Journal of Combinatorial Theory Series A

DOI: 10.1016/j.jcta.2026.106167

Authors: Primož Šparl, Jin-Xin Zhou

Institutions: University of Primorska, University of Ljubljana, Institute of Mathematics, Physics, and Mechanics, Beijing Jiaotong University

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,210

Funders: National Natural Science Foundation of China, Javna Agencija za Raziskovalno Dejavnost RS, Higher Education Discipline Innovation Project