Spectra of join of quasi-corona R graph

In this paper, we have determined the adjacency, the Laplacian and the signless Laplacian spectra of quasi-corona R-vertex join, represented by G?u?H and quasi-corona R-edge join, represented by G?e?H and obtain several adjacency, Laplacian and signless Laplacian cospectral of non-regular graphs. Further, we have also determined the Kirchhoff ?s indices, Laplacian-energy-like-invariant (LEL) and the number of spanning trees from Laplacian spectra.