Spectra of Graph Operations Based on Corona and Neighborhood Corona of Graph G and K1

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 paper we compute the adjacency spectrum (respectively, Laplacian spectrum, signless Laplacian) of four types of graph operations on G and H, called as Nvertex corona, C-vertex neighborhood corona, C-edge corona and N-edge corona, based on the corona and neighborhood corona of G and K1. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs.