Bounds for symmetric division deg index of graphs

Abstract

LetG = (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 = ? > 0, di = d(i), be a sequence of its vertex degrees with maximum degree ? and minimum degree ?. 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) = ?i~j d2i+d2j/didj, 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.