Spectra of generalized corona of graphs

Given simple graphs G,H1,…,Hn, where n=|V(G)|, the generalized corona, denoted G∘˜Λi=1nHi, is the graph obtained by taking one copy of graphs G,H1,…,Hn and joining the ith vertex of G to every vertex of Hi. In this paper, we determine and study the characteristic, Laplacian and signless Laplacian polynomial of G∘˜Λi=1nHi. This leads us to construct new pairs of cospectral, L-cospectral and Q-cospectral graphs. As an application, we give a simple proof for Csikvari's Lemma on eigenvalues of graphs.