Discrete Applied Mathematics 221 Glogić, Edin Zogić, Emir Glišović, Nataša Remarks on the upper bound for the Randic energy of bipartite graphs https://phaidrabg.bg.ac.rs/o:28918 doi:10.1016/j.dam.2016.12.005 ISSN: 0166-218X All rights reserved 2017 Keywords: Graph spectrum, graph energy, Randić matrix, Randić energy Abstract: Let G = (V , E), V = {1, 2, . . . , n} be a simple graph without isolated vertices, with n(n ≥ 3) vertices and m edges, whose vertex degrees are given in the following form d1 ≥ d2 ≥ • • • ≥ dn > 0. If A is the adjacency matrix, the Randić matrix R = ∥Rij∥ is defined in the following way Rij =1/√didj if vi and vj are adjacent and 0, otherwise. The eigenvalues of matrix R, ρ1 ≥ ρ2 ≥ • • • ≥ ρn, are called the Randić eigenvalues of graph G. The Randić energy of graph G, denoted by RE, is defined in the following way: RE = RE(G) =|ρi|. In this paper, upper bounds for graph invariant RE have been studied. info:eu-repo/semantics/article application/pdf 370516 bytes eng