On Randić energy

Abstract

The Randić matrix R=(rij) of a graph G whose vertex vi has degree di is defined by rij=1/ √didj if the vertices vi and v j are adjacent and rij=0 otherwise. The Randić energy RE is the sum of absolute values of the eigenvalues of R. RE coincides with the normalized Laplacian energy and the normalized signless-Laplacian energy. Several properties or R and RE are determined, including characterization of graphs with minimal RE. The structure of the graphs with maximal RE is conjectured. © 2013 Elsevier Inc. All rights reserved.