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Linear and non-linear inequalities on the inverse sum indeg index. (English) Zbl 1407.05058

Summary: 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 \(u \in V(G)\). In contemporary mathematical chemistry a large number of graph invariants of the form \(\sum_{u v \in E(G)} F(d_u, d_v)\) are studied. Among them the “inverse sum indeg index” ISI, for which \(F(d_u, d_v) = d_u d_v /(d_u + d_v)\), 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.

MSC:

05C07 Vertex degrees
05C90 Applications of graph theory
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

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References:

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