Distance spectrum of graph compositions

Indulal Gopalapillai

Abstract


The D-eigenvalues μ1, μ2, ..., μp of a graph G are the eigenvalues of its distance matrix D and form the distance spectrum or the D-spectrum.  In this paper we obtain the D-spectrum of the cartesian product if two distance regular graphs. The D-spectrum of the lexicographic product G[H] of two graphs G and H when H is regular is also obtained. The D-eigenvalues of the Hamming graphs Ham(d, n) of diameter d and order nd and those of the C4 nanotori, Tk,m,C4, are determined.

Keywords


Distance spectrum, Cartesian product, lexicographic product, Hamming graphs, C4 nanotori

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DOI: https://doi.org/10.26493/1855-3974.103.e09

ISSN: 1855-3974

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