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

Šparl, Primož (author), Zhou, Jin-Xin (author)

A graph is said to be half-arc-transitive if its automorphismgroup is transitive on the vertices and the edges of the graph but not on its arcs. Tetravalent half-arc-transitive graphsof 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 graphsof girth 5 is given, and as an application, two open questions from Antončič and Šparl (2023) [1] are answered.

• Language: English
• Keywords: Tetravalent graph, Half-arc-transitive, Girth 5
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 27 str.
• Numbering: art. 106167, Vol. 221
• PID: 20.500.12556/RUL-180459
• UDC: 519.17
• ISSN on article: 1096-0899
• DOI: 10.1016/j.jcta.2026.106167
• COBISS.SI-ID: 270921987
• Publication date in RUL: 10.03.2026

Record is a part of a journal

• Title: Journal of combinatorial theory
• Shortened title: J. comb. theory, Ser A
• Publisher: Elsevier
• ISSN: 1096-0899
• COBISS.SI-ID: 175260931

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: tetravalentni pol-lok-transitivni grafi, matematika