On symmetries of Cayley graphs and the graphs underlying regular maps

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dc.contributor.author Conder, Marston en
dc.date.accessioned 2012-03-30T08:21:58Z en
dc.date.issued 2009 en
dc.identifier.citation Journal of Algebra 321(11):3112-3127 2009 en
dc.identifier.issn 0021-8693 en
dc.identifier.uri http://hdl.handle.net/2292/16196 en
dc.description.abstract By definition, Cayley graphs are vertex-transitive, and graphs underlying regular or orientably-regular maps (on surfaces) are arc-transitive. This paper addresses questions about how large the automorphism groups of such graphs can be. In particular, it is shown how to construct 3-valent Cayley graphs that are 5-arc-transitive (in answer to a question by Cai Heng Li), and Cayley graphs of valency t3+1 that are 7-arc-transitive, for all t>0. The same approach can be taken in considering the graphs underlying regular or orientably-regular maps, leading to classifications of all such maps having a 1-, 4- or 5-arc-regular 3-valent underlying graph (in answer to questions by Cheryl Praeger and Sanming Zhou). en
dc.publisher Elsevier Inc. en
dc.relation.ispartofseries Journal of Algebra en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.sherpa.ac.uk/romeo/issn/0021-8693/ en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title On symmetries of Cayley graphs and the graphs underlying regular maps en
dc.type Journal Article en
dc.identifier.doi 10.1016/j.jalgebra.2008.04.016 en
pubs.begin-page 3112 en
pubs.volume 321 en
dc.rights.holder Copyright: Elsevier Inc. en
pubs.end-page 3127 en
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.subtype Article en
pubs.elements-id 89240 en
pubs.org-id Science en
pubs.org-id Mathematics en
pubs.record-created-at-source-date 2010-09-01 en

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