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

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 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ G 1 + G 2 , tensor product ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ G 1 ⊗ G 2 , Cartesian product ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ G 1 × G 2 , composition ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ G 1 ∘ G 2 , strong product ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ G 1 ∗ G 2 , disjunction ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ G 1 ∨ G 2 and symmetric difference ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ G 1 ⊕ G 2 will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.