1. Symmetries of the Woolly Hat graphsLeah Berman, Sergio Hiroki Koike Quintanar, Elías Mochán, Alejandra Ramos Rivera, Primož Šparl, Steve Wilson, 2024, original scientific article Abstract: 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.
Keywords: edge-transitive, vertex-transitive, tricirculant, Woolly Hat graphs
Published in RUP: 10.09.2025; Views: 530; Downloads: 7
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2. Linking rings structures and semisymmetric graphs : combinatorial constructionsPrimož Potočnik, Steve Wilson, 2018, original scientific article Keywords: graphs, automorphism group, symmetry, locally arc-transitive graphs, symmetric graphs, cycle structure, linking ring structure
Published in RUP: 03.01.2022; Views: 2446; Downloads: 19
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6. Arc-transitive cycle decompositions of tetravalent graphsŠtefko Miklavič, Primož Potočnik, Steve Wilson, 2008, original scientific article Abstract: A cycle decomposition of a graph ▫$\Gamma$▫ is a set ▫$\mathcal{C}$▫ of cycles of ▫$\Gamma$▫ such that every edge of ▫$\Gamma$▫ belongs to exactly one cycle in ▫$\mathcal{C}$▫. Such a decomposition is called arc-transitive if the group of automorphisms of ▫$\Gamma$▫ that preserve setwise acts transitively on the arcs of ▫$\Gamma$▫. In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining and enumerating arc-transitive cycle decompositions admitted by a given arc-transitive tetravalent graph. Among other results we show that a connected tetravalent arc-transitive graph is either 2-arc-transitive, or is isomorphic to the medial graph of a reflexible map, or admits exactly one cycle structure.
Keywords: mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps
Published in RUP: 15.10.2013; Views: 6923; Downloads: 91
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7. Seasonal variation of small mammals in the diet of the barn owl (Tyto alba) in the Drinos River valley, southern AlbaniaGligor Paspali, Selfo Oruçi, Mynyr Koni, I. Wilson, Boris Kryštufek, Ferdinand Bego, 2013, original scientific article Keywords: barn owl, Tyto alba, Insectivora, Rodentia, seasonal varation, Drinos valley, Gjirokastra, Albania
Published in RUP: 15.10.2013; Views: 7676; Downloads: 101
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8. Characterization of edge-transitive 4-valent bicirculantsIstván Kovács, Boštjan Kuzman, Aleksander Malnič, Steve Wilson, 2012, original scientific article Abstract: Bicirkulant je graf, ki dopušča avtomorfizem z natanko dvema orbitama vozlišč enake velikosti. V članku so karakterizirani vsi neizomorfni 4-valentni povezavno tranzitivni bicirkulanti. Posledično je izpeljana karakterizacija 4-valentnih ločno tranzitivnih dihedrantov.
Keywords: matematika, teorija grafov, štirivalenten graf, bicirkulantni graf, Cayleyev graf, povezavno tranzitiven graf, ločno tranzitiven graf, dihedrant, rose window graf, grupa avtomorfizmov
Published in RUP: 15.10.2013; Views: 6526; Downloads: 162
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