A forgotten topological index

Abstract

© 2015, Springer International Publishing Switzerland. In 1972, within a study of the structure-dependency of total (Formula presented.)-electron energy ((Formula presented.)), it was shown that (Formula presented.) 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 (Formula presented.), 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.