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    Cayley digraphs of finite abelian groups and monomial ideals

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    Identificadores
    URI: http://hdl.handle.net/10902/1634
    DOI: 10.1137/050646056
    ISSN: 1095-7146
    ISSN: 0895-4801
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    Author
    Gómez Pérez, DomingoAutoridad Unican; Gutiérrez Gutiérrez, JaimeAutoridad Unican; Ibeas Martín, Alvar JesúsAutoridad Unican
    Date
    2007
    Derechos
    © 2007 Society for Industrial and Applied Mathematics
    Publicado en
    SIAM Journal on Discrete Mathematics, 2007, 21(3), 763–784
    Publisher
    Society for Industrial and Applied Mathematics
    Palabras clave
    Monomial ideals
    Cayley digraph
    Gröbner bases
    Multiloop networks
    Abstract:
    In the study of double-loop computer networks, the diagrams known as L-shapes arise as a graphical representation of an optimal routing for every graph’s node. The description of these diagrams provides an efficient method for computing the diameter and the average minimum distance of the corresponding graphs. We extend these diagrams to multiloop computer networks. For each Cayley digraph with a finite abelian group as vertex set, we define a monomial ideal and consider its representations via its minimal system of generators or its irredundant irreducible decomposition. From this last piece of information, we can compute the graph’s diameter and average minimum distance. That monomial ideal is the initial ideal of a certain lattice with respect to a graded monomial ordering. This result permits the use of Gr¨obner bases for computing the ideal and finding an optimal routing. Finally, we present a family of Cayley digraphs parametrized by their diameter d, all of them associated to irreducible monomial ideals.
    Collections to which it belong
    • D20 Artículos [340]
    • D21 Artículos [233]

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    UNIVERSIDAD DE CANTABRIA

    Repositorio realizado por la Biblioteca Universitaria utilizando DSpace software
    Contact Us | Send Feedback
    Metadatos sujetos a:licencia de Creative Commons Reconocimiento 3.0 España