Constructing cospectral graphs via a new form of graph product

Michael Langberg, Dan Vilenchik

    Research output: Contribution to journalArticlepeer-review

    4 Scopus citations

    Abstract

    We present a new method to construct a family of co-spectral graphs. Our method is based on a new type of graph product that we define, the bipartite graph product, which may be of self-interest. Our method is different from existing techniques in the sense that it is not based on a sequence of local graph operations (e.g. Godsil–McKay switching). The explicit nature of our construction allows us, for example, to construct an infinite family of cospectral graphs and provide an easy proof of non-isomorphism. We are also able to characterize fully the spectrum of the cospectral graphs.

    Original languageEnglish
    Pages (from-to)1838-1852
    Number of pages15
    JournalLinear and Multilinear Algebra
    Volume66
    Issue number9
    DOIs
    StatePublished - 2 Sep 2018

    Keywords

    • 05C50
    • 05C76
    • Cospectral graphs
    • graph product

    ASJC Scopus subject areas

    • Algebra and Number Theory

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