Products of graphs and their spectra

Abstract

In this paper some new methods of constructing infinite families of cospectral graphs are presented. As an example of their application it is shown that given any graph G on n vertices one can construct at least $\left( {\begin{array}{*{20}c}{2n - 2} \\{n - 2} \\\end{array} } \right)$ non-isomorphic pairs of connected cospectral graphs on 3n vertices such that each member of each of the pairs contains three disjoint subgraphs isomorphic to G.

The same procedure can be used to construct pairs of non-isomorphic and non-cospectral graphs with the same spectral radius containing any two given graphs as disjoint induced subgraphs.