Bounds for symmetric division deg index of graphs

Abstract

Let G = (V, E) be a simple connected graph of order n (≥ 2) and size m, where V(G) = {1, 2,…, n}. Also let ∆ = d1 ≥ d2 ≥ · · · ≥ dn = δ > 0, di = d(i), be a sequence of its vertex degrees with maximum degree ∆ and minimum degree δ. The symmetric division deg index, SDD, was defined in [D. Vukičević, Bond additive modeling 2. Mathematical properties of max-min rodeg index, Croat. Chem. Acta 83 (2010) 261– d2i+d2j 273] as SDD = SDD(G) = (Formula presented), where i ~ j means that vertices i and j are adjacent. In this paper di dj we give some new bounds for this topological index. Moreover, we present a relation between topological indices of graph.