Spectra of new graph operations based on central graph

Abstract

In this paper, we introduce central vertex corona, central edge corona, and central edge neighborhood corona of graphs using central graph. Also, we determine their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum. From our results, it is possible to obtain infinitely many pairs of adjacency (respectively, Laplacian and signless Laplacian) cospectral graphs. As an application, we calculate the number of spanning trees and the Kirchhoff index of the resulting graphs.