1. On cubic vertex-transitive graphs of given girthEdward Tauscher Dobson, Ademir Hujdurović, Wilfried Imrich, Ronald Ortner, 2025, original scientific article Abstract: A set of vertices of a graph is distinguishing if the only automorphism that preserves it is the identity. The minimal size of such sets, if they exist, is the distinguishing cost. The distinguishing costs of vertex transitive cubic graphs are well known if they are 1-arc-transitive, or if they have two edge orbits and either have girth 3 or vertex-stabilizers of order 1 or 2. There are many results about vertex-transitive cubic graphs of girth 4 with two edge orbits, but for larger girth almost nothing is known about the distinguishing costs of such graphs. We prove that cubic vertex-transitive graphs of girth 5 with two edge orbits have distinguishing cost 2, and prove the non-existence of infinite 3-arc-transitive cubic graphs of girth 6.
Keywords: distinguishing number, distinguishing cost, vertex-transitive cubic graphs, automorphisms
Published in RUP: 27.08.2025; Views: 763; Downloads: 4
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3. The automorphism groups of non-edge transitive rose window graphsEdward Tauscher Dobson, István Kovács, Štefko Miklavič, 2015, original scientific article Abstract: In this paper, we determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we determine the isomorphism classes of non-edge-transitive rose window graphs.
Keywords: rose window graphs, automorphism group, isomorphism problem, vertex-transitive graph
Published in RUP: 31.12.2021; Views: 2668; Downloads: 44
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9. Imprimitive permutations in primitive groupsJoao Araújo, J. P. Araújo, Peter J. Cameron, Edward Tauscher Dobson, A. Hulpke, P. Lopes, 2017, original scientific article Keywords: primitive groups, imprimitive groups, GAP, permutation type
Published in RUP: 21.02.2018; Views: 4420; Downloads: 262
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