Linear and non-linear inequalities on the inverse sum indeg index

Abstract

Abstract 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 ∈ V ( G ) . In contemporary mathematical chemistry a large number of graph invariants of the form ∑ u v ∈ 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.