On the Co-PI and Laplacian Co-PI eigenvalues of a graph

Abstract

In this paper we present an equivalent definition of Co-PI index and then determine the eigenvalues of Co-PI matrices and their Laplacians of Cartesian product graphs, including bounds on the second and third Co-PI spectral moment of a graph. The explicit formulae for the Co-PI index of Cartesian product graphs are also presented. © 2012 Elsevier B.V. All rights reserved.