On Randic Energy of Graphs

Let G = (V, E) be a simple graph with vertex set V (G) = (v(1,) v(2),..., v(n),} and edge set E(G). The Randie matrix R = (r(ij)) of a graph G whose vertex v(i) has degree di is defined by r(ij) = 1/root d(i)d(j) if the vertices v(i) and v(j) are adjacent and r(ij) = 0 otherwise. The Randie energy RE 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.