On degree based topological indices of certain nanotubes

Abstract

A numeric quantity which characterise the whole structure of a graph is called a topological index. The concept of atom-bond connectivity (ABC) and geometric-arithmetic (GA) topological indices were established in chemical graph theory based on vertex degrees. Later on, other versions of these indices were introduced and some of the versions of these indices are recently designed. Let H be a graph, then the general definitions of these indices are as follows: ABC(H) = ∑ab∈E(H) √(Qa + Qb - 2)/(QaQb), and GA(H) = ∑ab∈E(H)2√QaQb/(Qa + Qb/), where Qa is the quantity which is uniquely related to the vertex a. Carbon nanotubes which are actually carbon allotropes, have applications in the fields such as electronics, materials science, optics, nanotechnology, and architecture. To study and compute topological indices of nanostructures is a respected problem in nanotechnology. In this article, we compute atom-bond connectivity (ABC), geometric-arithmetic (GA), and Randić indices of H-Naphtalenic nanotubes and TUC4[mo, n] nanotube. We also compute fourth version of atom-bond connectivity (ABC4) index and fifth version of geometric-arithmetic (GA5) index for these families of nanotubes.