20.500.12556/RUL-128564 Half-arc-transitive graphs and the Fano plane 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. half-arc-transitive Fano plane Heawood graph construction matematika true false true Angleški jezik Slovenski jezik Članek v reviji 2021-07-20 04:42:54 2021-08-16 11:33:44 2025-09-15 09:39:45 0000-00-00 00:00:00 2021 0 0 Str. 987-1012 iss. 3 Vol. 37 2021 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 2022-05-01 519.17 1435-5914 10.1007/s00373-021-02298-6 67311619 Macaj_Sparl_Half_Arc.pdf Macaj_Sparl_Half_Arc.pdf 1 221124FB6EC66A76A1C618CA77312267 5b328bab613c203f9669ac2554814bb9315cb1955ac0afe3b7fcc2354332b3d8 8d2052e6-1ab6-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=207680 https://link.springer.com/article/10.1007/s00373-021-02298-6 0 aae1a30c-9206-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=217448 Pedagoška fakulteta 0 0 0