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Let G be a graph with vertex set V(G) and edge set E(G), and let d u be the degree of the vertex u is an element of V(G). In contemporary mathematical chemistry a large number of graph invariants of the form Sigma(uv is an element of E(G)) F(d(u), d(v)) are studied. Among them the "inverse sum indeg index" ISI, for which F(d(u),d(v)) = d(u) d(v)/(d(u) + dv), was found to have outstanding applicative properties. The aim of this paper is to obtain new inequalities for ISI and to characterize graphs extremal with respect to them. Some of these inequalities generalize and improve previous results. (C) 2018 Elsevier B.V. All rights reserved.
degree (of vertex of graph); degree-based graph invariant; degree-based topological index; inverse sum indeg index; inverse sum index; zagreb; graphs