(untitled) (Journal of Mathematical Study, 2018)
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.