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2. On colour-preserving automorphisms of Cayley graphsAdemir Hujdurović, Klavdija Kutnar, Dave Witte Morris, Joy Morris, 2016, original scientific article Abstract: We study the automorphisms of a Cayley graph that preserve its natural edge-colouring. More precisely, we are interested in groups ▫$G$▫, such that every such automorphism of every connected Cayley graph on ▫$G$▫ has a very simple form: the composition of a left-translation and a group automorphism. We find classes of groups that have the property, and we determine the orders of all groups that do not have the property. We also have analogous results for automorphisms that permute the colours, rather than preserving them. Keywords: Cayley graph, automorphism, colour-preserving, colour-permuting Published in RUP: 03.01.2022; Views: 787; Downloads: 18 Full text (412,93 KB) |
3. The automorphism groups of non-edge transitive rose window graphsEdward 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: 995; Downloads: 19 Full text (275,74 KB) |
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8. Hamilton cycles in primitive vertex-transitive graphs of order a product of two primes - the case PSL(2, q[sup]2) acting on cosets of PGL(2, q)Shao Fei Du, Klavdija Kutnar, Dragan Marušič, 2020, original scientific article Abstract: A step forward is made in a long standing Lovász problem regarding hamiltonicity of vertex-transitive graphs by showing that every connected vertex-transitive graph of order a product of two primes arising from the group action of the projective special linear group PSL▫$(2, q^2)$▫ on cosets of its subgroup isomorphic to the projective general linear group PGL$(2, q)$ contains a Hamilton cycle. Keywords: vertex-transitive graph, Hamilton cycle, automorphism group, orbital graph Published in RUP: 20.07.2020; Views: 1402; Downloads: 46 Full text (365,31 KB) |
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