Half-arc-transitive graphs and the Fano plane

Mačaj, Martin (avtor), Šparl, Primož (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: half-arc-transitive, Fano plane, Heawood graph, construction
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2021
• Št. strani: Str. 987-1012
• Številčenje: Vol. 37, iss. 3
• PID: 20.500.12556/RUL-128564
• UDK: 519.17
• ISSN pri članku: 1435-5914
• DOI: 10.1007/s00373-021-02298-6
• COBISS.SI-ID: 67311619
• Datum objave v RUL: 16.08.2021

Gradivo je del revije

• Naslov: Graphs and combinatorics
• Skrajšan naslov: Graphs comb.
• Založnik: Springer Nature
• ISSN: 1435-5914
• COBISS.SI-ID: 513673497

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: matematika