Spectra of Corona Based on the Total Graph

For two simple connected graphs G(1) and G(2), we introduce a new graph operation called the total corona G(1) circle star G(2) on G(1) and G(2) involving the total graph of G(1). Subsequently, the adjacency (respectively, Laplacian and signless Laplacian) spectra of G(1) circle star G(2) are determined in terms of these of a regular graph G(1) and an arbitrary graph G(2). As applications, we construct infinitely many pairs of adjacency (respectively, Laplacian and signless Laplacian) cospectral graphs. Besides we also compute the number of spanning trees of G(1) circle star G(2).