Computation of the Forgotten Topological Index and Co-Index for Carbon Base Nanomaterial

Abstract

Molecular topological indices are numerical descriptor of molecular structure obtained via molecular graph G. The forgotten topological index F(G) is a vertex degree based topological index and it can be expressed with $F\left(G\right)=\sum {d\left(v\right)}^3=\sum \left({d\left(u\right)}^2+{d\left(v\right)}^2\right),$ where d(u) denotes the degree of u. The forgotten co-index Co-F(G) is defined as the sum of squares of a graph’s vertex degrees which is not adjacent. In this study, the F(G) and Co-F(G) index of HAC₅C₇, HAC₅C₆C₇, linear [n]-phenylenes and cyclic phenylenes nanostructures are computed for possible works in the properties of molecules such as structure–property relationship. In addition, polynomials of the forgotten index and co-index are found for these nanostructures.

Keywords:

• Forgotten topological coindex
• forgotten topological index
• graph theory
• nanostructure
• phenylenes
• topological index

Acknowledgment

We would like to add that the results of the Ref. 24 and the results of our study are completely different. Because, the number of vertices and edges of the nanostructures were handled differently. In the article, all calculation were done only for the F-index but we did all calculation for both F-index and F-coindex.

Disclosure statement

The authors declare that there is no conflict of interest regarding the publication of this article.