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New inequalities involving the geometric-arithmetic index

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2017
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MATCH
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Let G = (V, E) be a simple connected graph and di be the degree of its ith vertex. In a recent paper [J. Math. Chem. 46 (2009) 1369-1376] the first geometricarithmetic index of a graph G was defined as GA1 = X uv∈E 2 √ dudv du + dv . This graph invariant is useful for chemical proposes. The main use of GA1 is for designing so-called quantitative structure-activity relations and quantitative structureproperty relations. In this paper we obtain new inequalities involving the geometricarithmetic index GA1 and characterize the graphs which make the inequalities tight. In particular, we improve some known results, generalize other, and we relate GA1 to other well-known topological indices.
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Graph invariant, Vertex-degree-based graph invariant, Topological index, Geometric-arithmetic index
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Rodrígez, J. M., Rodríguez, J. A. & Sigarreta, J. M. (2017). New Inequalities Involving the Geometric–Arithmetic Index. MATCH Communications in Mathematical and in Computer Chemistry, 78(2), 361-374.