More on Energy and Randi´c Energy of Specific Graphs

Abstract

Let G be a simple graph of order n. The energy E(G) of G is the sum of the absolute values of the eigenvalues of G. The Randi´c matrix of G, denoted by R(G), is defined as the n×n matrix whose (i, j)- entry is (didj ) −1 2 if vi and vj are adjacent and 0 for another cases. The Randi´c energy RE(G) of G is the sum of absolute values of the eigenvalues of R(G). In this paper we compute the energy and the Randi´c energy for certain graphs. We also propose a conjecture on the Randi´c energy