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dc.contributor.authorThomson, Alisonen_US
dc.contributor.authorZHOU, SANMINGen_US
dc.date.accessioned2014-05-22T07:43:15Z
dc.date.available2014-05-22T07:43:15Z
dc.date.issued2008en_US
dc.identifier1446-7887
dc.identifier.citationThomson, A., & Zhou, S. (2008). Frobenius circulant graphs of valency four. Journal of the Australian Mathematical Society, 85(2), 269-282.en_US
dc.identifier.urihttp://hdl.handle.net/11343/33003
dc.description© 2008 Australian Mathematical Society. Online edition of the journal is available at http://journals.cambridge.org/JAZen_US
dc.description.abstractA first kind Frobenius graph is a Cayley graph Cay.K; S/ on the Frobenius kernel of a Frobenius group K o H such that S D aH for some a 2 K with haH i D K, where H is of even order or a is an involution. It is known that such graphs admit ‘perfect’ routing and gossiping schemes. A circulant graph is a Cayley graph on a cyclic group of order at least three. Since circulant graphs are widely used as models for interconnection networks, it is thus highly desirable to characterize those which are Frobenius of the first kind. In this paper we first give such a characterization for connected 4-valent circulant graphs, and then describe optimal routing and gossiping schemes for those which are first kind Frobenius graphs. Examples of such graphs include the 4-valent circulant graph with a given diameter and maximum possible order.en_US
dc.languageengen_US
dc.publisherCambridge University Pressen_US
dc.subjectCayley graphen_US
dc.subjectcirculant graphen_US
dc.subjectmulti-loop networken_US
dc.subjectdouble-loop networken_US
dc.subjectFrobenius groupen_US
dc.subjectFrobenius graphen_US
dc.subjectcomplete rotationen_US
dc.subjectgossipingen_US
dc.subjectminimum gossip timeen_US
dc.subjectroutingen_US
dc.subjectedgeforwardingen_US
dc.subjectindexen_US
dc.subjectarc-forwarding indexen_US
dc.titleFrobenius circulant graphs of valency fouren_US
dc.typeJournal Articleen_US
dc.identifier.doi10.1017/S1446788708000979
melbourne.peerreviewPeer Revieweden_US
melbourne.affiliationThe University of Melbourneen_US
melbourne.affiliation.departmentDepartment of Mathematics and Statisticsen_US
melbourne.publication.statusPublisheden_US
melbourne.source.titleJournal of the Australian Mathematical Societyen_US
melbourne.source.volume85en_US
melbourne.source.issue2en_US
melbourne.source.pages269-282en_US
melbourne.elementsidNA
melbourne.contributor.authorTHOMSON, ALISON
melbourne.contributor.authorZhou, Sanming
melbourne.accessrightsOpen Access


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