A forgotten topological index

Abstract

In 1972, within a study of the structure-dependency of total π -electron energy (E), it was shown that 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 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.

A short note on hyper Zagreb index

“…In 2015, Fortula and Gutman [12,13] introduced the forgotten topological index and for α = 2 in (1.1) turns it as a very special case formula, defined by…”

“…Note that forgotten topological index [12] has only few lower bounds. At first, we give an upper bound for M 3 1 (G) which leads to the upper bound for χ 2 (G).…”

Upper bounds for the extended energy of graphs and some extended equienergetic graphs

“…The forgotten topological index F (G) [8] and the inverse degree sum r(G) [16] of a graph G are two degree based topological indices. These are defined as…”

Computing F-Index of Different Corona Products of Graphs

“…Furtula and Gutman in 2015 [12] studied this index again and named as "forgotten topological index" or "F-index". In that paper they showed that the predictive ability of this index is almost similar to that of first Zagreb index and for the entropy and acetic factor, both of them yield correlation coefficients greater than 0.95.…”