The corona G◦H of two graphs G and H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining each i-th vertex of G to every vertex in the i-th copy of H. The neighborhood coronaG⋆H of two graphs G and H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the neighbors of the i-th vertex of G to every vertex in the i-th copy of H. In this p...

A 2-edge-covering between G and H is an onto homomorphism from the vertices of G to the vertices of H so that each edge is covered twice and edges in H can be lifted back to edges in G. In this note we show how to compute the spectrum of G by computing the spectrum of two smaller graphs, namely a (modified) form of the covered graph H and another graph which we term the anti-cover. This is done...

We study the relationship between the arithmetic and the spectrum of the Laplacian for manifolds arising from congruent arithmetic subgroups of SL(1, D), where D is an indefinite quaternion division algebra defined over a number field F . We give new examples of isospectral but non-isometric compact, arithmetically defined varieties, generalizing the class of examples constructed by Vigneras. T...