Spectra of M-generalized corona of graphs constrained by vertex subsets

In this paper, we define a new type of corona operation which generalizes almost all the variants of corona of graphs defined in the literature. As particular cases of this construction, we define several variants of corona of graphs and some new unary graph operations. We determine the generalized characteristic polynomial of this constructed graph. Consequently, we derive the characteristic polynomials of the adjacency matrix and Laplacian matrix of the graphs constructed by the newly defined, and almost all the existing variants of corona of graphs. As applications of these results, we construct infinite families of integral graphs and cospectral graphs.