A forgotten topological index

Abstract

In 1972, within a study of the structure-dependency of total $\pi$-electron energy (${\mathcal {E}}$), it was shown that ${\mathcal {E}}$ depends on the sum of squares of the vertex degrees of the molecular graph (later named first Zagreb index), and thus provides a measure of the branching of the carbon-atom skeleton. In the same paper, also the sum of cubes of degrees of vertices of the molecular graph was shown to influence ${\mathcal {E}}$, but this topological index was never again investigated and was left to oblivion. We now establish a few basic properties of this “forgotten topological index” and show that it can significantly enhance the physico-chemical applicability of the first Zagreb index.