Frobenius circulant graphs of valency four
AuthorThomson, Alison; ZHOU, SANMING
Source TitleJournal of the Australian Mathematical Society
PublisherCambridge University Press
AffiliationDepartment of Mathematics and Statistics
Document TypeJournal Article
CitationsThomson, A., & Zhou, S. (2008). Frobenius circulant graphs of valency four. Journal of the Australian Mathematical Society, 85(2), 269-282.
Access StatusOpen Access
© 2008 Australian Mathematical Society. Online edition of the journal is available at http://journals.cambridge.org/JAZ
A 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.
KeywordsCayley graph; circulant graph; multi-loop network; double-loop network; Frobenius group; Frobenius graph; complete rotation; gossiping; minimum gossip time; routing; edgeforwarding; index; arc-forwarding index
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