552 KB0 KB176 KB6 KB2023Berman, LeahKoike Quintanar, Sergio HirokiMochán, ElíasRamos Rivera, AlejandraŠparl, PrimožWilson, Steveštevilka:224 str.letnik:7DOI:10.26493/2590-9770.1617.83cCOBISSID_HOST:188232195ISSN:2590-9770URN:URN:NBN:SI:doc-R17TQ25PenFakulteta za matematiko, naravoslovje in informacijske tehnologijeThe art of discrete and applied mathematicsedge-transitivetricirculantvertex-transitiveWoolly Hat graphsSymmetries 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 onesTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije