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. Vukicˇevic´, Bond additive modeling 2. Mathematical properties of max-min rodeg index, Croat. Chem. Acta 83 (2010) 261– 273] as SDD = SDD(G) = ∑ i∼ j d2i +d 2 j did j , where i ∼ j means that vertices i and j are adjacent. In this paper we give some new bounds for this topological index. Moreover, we present a relation between topological indices of graph.