Half-arc-transitive graphs and the fano plane

Martin Mačaj (Author), Primož Šparl (Author)

Abstract

A subgroup G of the automorphism group of a graph Γ acts half-arc-transitively on Γ if the natural actions of G on the vertex-set and edge-set of Γ are both transitive, but the natural action of G on the arc-set of Γ is not transitive. When G = Aut(Γ) the graph Γ is said to be half-arc-transitive. Given a bipartite cubic graph with a certain degree of symmetry two covering constructions that provide infinitely many tetravalent graphs admitting half-arc-transitive groups of automorphisms are introduced. Symmetry properties of constructed graphs are investigated. In the second part of the paper the two constructions are applied to the Heawood graph, the well-known incidence graph of the Fano plane. It is proved that the members of the infinite family resulting from one of the two constructions are all half-arc-transitive, and that the infinite family resulting from the second construction contains a mysterious family of arc-transitive graphs that emerged within the classification of tightly attached half-arc-transitive graphs of valence 4 back in 1998 and 2008.

Keywords

half-arc-transitive;fano plane;Heawood graph;construction;

Data

Language:	English
Year of publishing:	2021
Typology:	1.01 - Original Scientific Article
Organization:	UL PEF - Faculty of Education
Publisher:	Tokyo: Springer Japan
UDC:	519.17
COBISS:	67311619
ISSN:	1435-5914
Views:	2069
Downloads:	222
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Article
Embargo end date (OpenAIRE):	2022-05-01
Pages:	str. 987-1012
Volume:	ǂVol. ǂ37
Issue:	ǂissue ǂ3
Chronology:	2021
DOI:	10.1007/s00373-021-02298-6
ID:	13153397