On the path energy of some graphs

Abstract

Let G be a graph with vertex set V(G) = {v1, v2, ..., vn}. We define a matrix whose (i, j)^th entry is the maximum number of vertex disjoint paths between the corresponding vertices if they are adjacent and is zero otherwise. We call this matrix as path matrix of G and its eigenvalues as path eigenvalues of G. In this paper, we investigate path eigenvalues and path energy of some graphs.