The forgotten index of complement graph operations and its applications of molecular graph

Abstract

A topological index of graph \(G\) is a numerical parameter related to graph which characterizes its molecular topology and is usually graph invariant. Topological indices are widely used to determine the correlation between the specific properties of molecules and the biological activity with their configuration in the study of quantitative structure-activity relationships (QSARs). In this paper some basic mathematical operations for the forgotten index of complement graph operations such as join \(\overline {G_1+G_2}\), tensor product \(\overline {G_1 \otimes G_2}\), Cartesian product \(\overline {G_1\times G_2}\), composition \(\overline {G_1\circ G_2}\), strong product \(\overline {G_1\ast G_2}\), disjunction \(\overline {G_1\vee G_2}\) and symmetric difference \(\overline {G_1\oplus G_2}\) will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.