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 ⊛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 ⊛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 ⊛G 2 .