Distance spectrum of graph compositions

Indulal Gopalapillai


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.


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

Full Text:


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

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications