On an old/new degree-based topological index

Abstract

Let \(G\) be a graph with vertex set \(V(G)\) and let \(d(x)\) be the degree of the vertex \(x \in V(G)\). The graph invariant \(F = \sum_{x\in V(G)} d(x)^3\) played some role in a paper published in 1972, but has not attracted any attention until quite recently. In 2014 an unexpected chemical application of the \(F\)-index was discovered, which motivated us to establish its basic mathematical properties. Results obtained along these lines are presented