2018 info:eu-repo/semantics/article https://phaidrabg.bg.ac.rs/o:28913 doi:10.5937/SPSUNP1802099Z ISSN: 2217-5539 Abstract: Let G = (V, E), V = {1, 2, . . . , n}, be a simple graph of order n and size m, without isolated vertices. Denote by ∆ = d1 ≥ d2 ≥ • • • ≥ dn = d > 0, di = d(i), a sequence of its vertex degrees. If vertices i and j are adjacent, we write i ∼ j. With TI we denote a topological index that can be represented as T I = T I(G) = ∑▒〖F(di,d j),〗 where F is an appropriately chosen function with the property F(x, y) = F(y, x). Randić degree–based adjacency matrix RA = (ri j) is defined as rij = F(di,d j )/didj if i ∼ j, and 0 otherwise. Denote by fi, i = 1, 2, . . . , n, the eigenvalues of RA. The Randić degree-based energy of graph could be defined as RE_TI=RE_TI(G)= ∑▒〖| fi|.〗 Upper and lower bounds for RET I are obtained. Zogić, Emir Borovićanin, Bojana Milovanović,, Emina Milovanović, Igor Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics 10(2) Randić degree-based energy of graphs All rights reserved eng application/pdf 52761 bytes Keywords: Topological indices, vertex degree, Randi ́c degree-based energy (of graph)