The two Zagreb indices M 1 = ∑ v d(v) 2 and M 2 = ∑ uv d(u) d(v) are vertex-degree-based graph invariants that have been introduced in the 1970s and extensively studied ever since. In the last few years, a variety of modifications of M 1 and M 2 were put forward. The present survey of these modified Zagreb indices outlines their main mathematical properties, and provides an exhaustive bibliography.
Let G = (V, E) be a simple connected graph of order n (≥ 2) and size m, where V(G) = {1, 2,. .. , n}. Also let ∆ = d 1 ≥ d 2 ≥ • • • ≥ d n = δ > 0, d i = 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) 261-273] as SDD = SDD(G) = i∼ j d 2 i +d 2 j d i d 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.
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