Laplacian and Signless Laplacian Characteristic Polynomial of Generalized Subdivision Corona Vertex Graph

Abstract

Let \(G\) be a graph with \(n\) vertices, \(\mathcal{G}(G)\) the subdivision graph of \(G\). \(V(G)\) denotes the set of original vertices of \(G\). The generalized subdivision corona vertex graph of \(G\) and \(H_1, H_2, \ldots, H_n\) is the graph obtained from \(\mathcal{G}(G)\) and \(H_1, H_2, \ldots, H_n\) by joining the \(i\)th vertex of \(V(G)\) to every vertex of \(H_i\). In this paper, we determine the Laplacian (respectively, the signless Laplacian) characteristic polynomial of the generalized subdivision corona vertex graph. As an application, we construct infinitely many pairs of cospectral graphs.