FROBENIUS CIRCULANT GRAPHS OF VALENCY FOUR

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    Author
    Thomson, A; Zhou, S
    Date
    2008-10-01
    Source Title
    Journal of the Australian Mathematical Society
    Publisher
    CAMBRIDGE UNIV PRESS
    University of Melbourne Author/s
    Zhou, Sanming; THOMSON, ALISON
    Affiliation
    Department of Mathematics and Statistics
    Metadata
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    Document Type
    Journal Article
    Citations
    Thomson, 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 Status
    Open Access
    URI
    http://hdl.handle.net/11343/33003
    DOI
    10.1017/S1446788708000979
    Description

    © 2008 Australian Mathematical Society. Online edition of the journal is available at http://journals.cambridge.org/JAZ
    Abstract
    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.
    Keywords
    Cayley 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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