Distance spectrum of graph compositions

Abstract

The D -eigenvalues μ 1 , μ 2 , ..., μ p 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 n d and those of the C 4 nanotori, T k , m , C 4 , are determined.