FROBENIUS CIRCULANT GRAPHS OF VALENCY FOUR
AuthorThomson, A; Zhou, S
Source TitleJournal of the Australian Mathematical Society
PublisherCAMBRIDGE UNIV 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), pp.269-282. https://doi.org/10.1017/S1446788708000979.
Access StatusOpen Access
© 2008 Australian Mathematical Society. Online edition of the journal is available at http://journals.cambridge.org/JAZ
Abstract A first kind Frobenius graph is a Cayley graph Cay(K,S) on the Frobenius kernel of a Frobenius group $K \rtimes H$ such that S=aH for some a∈K with 〈aH〉=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
- Click on "Export Reference in RIS Format" and choose "open with... Endnote".
- Click on "Export Reference in RIS Format". Login to Refworks, go to References => Import References