Abstract

Let G be a simple undirected graph of order n with vertex set V(G) = {v1,v2, . . . , vn}. vml. Let d(i) the degree of the vertex vi. The RandiC matrix R = (r(i),j) of G is the square matrix of order n whose (i, j)-entry is equal to 1 if the vertices vi and vj are adjacent, and zero otherwise. The RandiC energy is the sum of the absolute values of the eigenvalues of R. Let X, Y, and Z be matrices, such that X Y = Z. Ky Fan established an inequality between the sum of singular values of X, Y, and Z. We apply this inequality to obtain bounds on Randle energy. We also present results pertaining to the energy of a symmetric partitioned matrix, as well as an application to the coalescence of graphs. (C) 2014 Elsevier Inc. All rights reserved.