Some new bounds on Randić energy Kragujevac Journal of Mathematics 43(3) Zogić, Emir Borovićanin, Bojana Keywords: Normalized Laplacian matrix, Randić matrix, Randić energy All rights reserved application/pdf 404078 bytes eng https://phaidrabg.bg.ac.rs/o:28911 ISSN: 1450-9628 info:eu-repo/semantics/article 2019 Abstract: Let G = (V , E) be a simple graph of order n with vertex set V =V (G) = {v1, v2, . . . , vn} and edge set E = E(G). Let di be the degree of the vertex vi in G for i = 1, 2, . . . , n. The Randić matrix R = ∥Rij∥ is defined by Rij =1/√didj if vi and vj are adjacent and 0, otherwise. The eigenvalues of matrix R, denoted by ρ1, ρ2, . . . , ρn, are called the Randić eigenvalues of graph G. The Randić energy of graph G, denoted by RE, is defined as RE = RE(G) =∑|ρi|. In this paper we establish some new upper and lower bounds on Randić energy.