Spectra of Corona Based on the Total Graph

For two simple connected graphs G1 and G2, we introduce a new graph op- eration called the total corona G1⊛G2 on G1 and G2 involving the total graph of G1. Subsequently, the adjacency (respectively, Laplacian and signless Laplacian) spectra of G1⊛G2 are determined in terms of these of a regular graph G1 and an arbitrary graph G2. As applications, we construct infinitely many pairs of adjacency (respec- tively, Laplacian and signless Laplacian) cospectral graphs. Besides we also compute the number of spanning trees of G1⊛G2. AMS subject classifications: 05C50, 05C90