Martin Mačaj (Avtor), Primož Šparl (Avtor)

Povzetek

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.

Ključne besede

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

Podatki

Jezik: Angleški jezik
Leto izida:
Tipologija: 1.01 - Izvirni znanstveni članek
Organizacija: UL PEF - Pedagoška fakulteta
Založnik: Tokyo: Springer Japan
UDK: 519.17
COBISS: 67311619 Povezava se bo odprla v novem oknu
ISSN: 1435-5914
Št. ogledov: 2069
Št. prenosov: 222
Ocena: 0 (0 glasov)
Metapodatki: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Ostali podatki

Sekundarni jezik: Slovenski jezik
Sekundarne ključne besede: mathematics;matematika;
Vrsta datoteke: application/pdf
Vrsta dela (COBISS): Članek v reviji
Konec prepovedi (OpenAIRE): 2022-05-01
Strani: str. 987-1012
Letnik: ǂVol. ǂ37
Zvezek: ǂissue ǂ3
Čas izdaje: 2021
DOI: 10.1007/s00373-021-02298-6
ID: 13153397