The Y-Index of Some Complement Graph Structures and Their Applications of Nanotubes and Nanotorus

Abstract

Topological descriptors play a significant role in chemical nanostructures. These topological measures have explicit chemical uses in chemistry, medicine, biology, and computer sciences. This study calculates the Y-index of some graphs and complements graph operations such as join, tensor and Cartesian and strong products, composition, disjunction, and symmetric difference between two simple graphs. Moreover, the Y-polynomial of titania nanotubes and the formulae for the Y-index, Y-polynomial, F-index, F-polynomial, and Y-coindex of the $\text{HA}{\mathrm{C}}_5{\mathrm{C}}_7\left[q,p\right]$ and $\text{HA}{\mathrm{C}}_5{\mathrm{C}}_6{\mathrm{C}}_7\left[q,p\right]$ nanotubes and their molecular complement graphs have been investigated.