Vertex-transitive digraphs with extra automorphisms that preserve the natural arc-colouring

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dc.contributor.authorDobson, Ted
dc.contributor.authorHujdurovic, Ademir
dc.contributor.authorKutnar, Klavdija
dc.contributor.authorMorris, Joy
dc.date.accessioned2018-07-06T20:30:32Z
dc.date.available2018-07-06T20:30:32Z
dc.date.issued2017
dc.descriptionDiamond open accessen_US
dc.description.abstractIn a Cayley digraph on a group G, if a distinct colour is assigned to each arc-orbit under the left-regular action of G, it is not hard to show that the elements of the left-regular action of G are the only digraph automorphisms that preserve this colouring. In this paper, we show that the equivalent statement is not true in the most straightforward generalisation to G-vertex-transitive digraphs, even if we restrict the situation to avoid some obvious potential problems. Specifically, we display an infinite family of 2-closed groups G, and a G-arc-transitive digraph on each (without any digons) for which there exists an automorphism of the digraph that is not an element of G (it is an automorphism of G). Since the digraph is G-arc-transitive, the arcs would all be assigned the same colour under the colouring by arc-orbits, so this digraph automorphism is colour-preserving.en_US
dc.description.peer-reviewYesen_US
dc.identifier.citationDobson, T., Hujdurovic, A., Kutnar, K., & Morris, J. (2017). Vertex-transitive digraphs with extra automorphisms that perserve the natural arc-colouring. Australasian Journal of Combinatorics, 67(2), 88-100en_US
dc.identifier.urihttps://hdl.handle.net/10133/5157
dc.language.isoen_USen_US
dc.publisherThe University of Queensland, Centre for Discrete Mathematics and Computingen_US
dc.publisher.departmentDepartment of Mathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.publisher.institutionMississippi State Universityen_US
dc.publisher.institutionUniversity of Primoskaen_US
dc.publisher.institutionUniversity of Lethbridgeen_US
dc.subjectVertex-transitive graphsen_US
dc.subjectDigraphsen_US
dc.subjectAutomorphismen_US
dc.subjectColour preservingen_US
dc.subjectArc-orbiten_US
dc.subjectCaleyen_US
dc.subject.lcshAutomorphisms
dc.subject.lcshDirected graphs
dc.subject.lcshGraph theory
dc.subject.lcshGroup theory
dc.subject.lcshCombinatorial analysis
dc.subject.lcshCaley graphs
dc.titleVertex-transitive digraphs with extra automorphisms that preserve the natural arc-colouringen_US
dc.typeArticleen_US
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