Recall that the spectrum (Laplacian spectrum resp.) of a simple undirected graph is the spectrum of its adjacency matrix (Laplcian matrix resp.).
Moreover, many products of graphs have been introduced and studied by mathematicians, the standard ones are : cartisien, lexicographic, direct and strong product of graphs.
Mathematicians like R.B. Bapat, Cardoso et al... have been specifically interested in finding the characteristic polynomial, eigenvalues, laplacian eigenvalues of such products, also sometimes if they were not able to find the spectrum explicitly, they search for the characteristic polynomial or they talk about some subset of the spectrum they found.
If someone could please explain what is the motivation behind finding the spectrum (Laplacian resp.) of such products of graphs. Thank you.