Bounds for Symmetric Division Deg Index of Graphs

Let G = (V, E) be a simple connected graph of order n (>= 2) and size m, where V(G) = {1, 2, ..., n}. Also let Delta = d(1) >= d(2) >= ... >= d(n) = delta > 0, d(i) = d(i), be a sequence of its vertex degrees with maximum degree A and minimum degree 6. The symmetric division deg index, SDD, was defined in [D. VukiCevic, Bond additive modeling 2. Mathematical properties of max-min rodeg index, Croat. Chem. Acta 83 (2010) 261-273) as SDD = SDD(G) = Sigma(i similar to j) d(i)(2)+d(j)(2)/d(i)d(j), where i similar to 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.