20.500.12556/DiRROS-20518 Symmetries of the Woolly Hat graphs A graph is edge-transitive if the natural action of its automorphism group on its edge set is transitive. An automorphism of a graph is semiregular if all of the orbits of the subgroup generated by this automorphism have the same length. While the tetravalent edge-transitive graphs admitting a semiregular automorphism with only one orbit are easy to determine, those that admit a semiregular automorphism with two orbits took a considerable effort and were finally classified in 2012. Of the several possible different "types" of potential tetravalent edge-transitive graphs admitting a semiregular automorphism with three orbits, only one "type" has thus far received no attention. In this paper we focus on this class of graphs, which we call the Woolly Hat graphs. We prove that there are in fact no edge-transitive Woolly Hat graphs and classify the vertex-transitive ones. edge-transitive vertex-transitive tricirculant Woolly Hat graphs true false true Angleški jezik Ni določen Neznano 2024-10-07 11:18:56 2024-10-07 11:18:56 2024-10-08 03:35:23 0000-00-00 00:00:00 2024 0 0 24 str. no. 2, [article no.] P2.06 Vol. 7 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-01-01 519.17 2590-9770 10.26493/2590-9770.1617.83c 188232195 adam_1617.pdf adam_1617.pdf 1 680BD2717ABDA58A0B26110444946330 9147466c1910c7a5f625702d4813c32d0d16ff14eccc23e09944e000779118ef 63a6c8e0-848d-11ef-a5bf-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=28927 https://adam-journal.eu/index.php/ADAM/article/view/1617 1 2f163085-848d-11ef-a5bf-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=28926 Inštitut za matematiko, fiziko in mehaniko 0 0 0