On Randic Energy of Graphs

Abstract

Let G =( V, E )b e as i mple graph with vertex set V (G )= {v1 ,v 2 ,..., vn} and edge set E(G). The Randic matrix R =( rij) of a graph G whose vertex vi has degree di is defined by rij =1 / � didj if the vertices vi and vj are adjacent and rij = 0 otherwise. The Randice nergyRE is the sum of absolute values of the eigenvalues of R. We provide lower and upper bounds for RE in terms of no. of vertices, maximum degree, minimum degree and the determinant of the adjacency matrix of graphs G.