Two Types of Geometric–Arithmetic Index of V–phenylenic Nanotube

Abstract

The concept of geometric-arithmetic indices was introduced in the chemical graph theory. These indices are defined by the following general formula:     ) Q is some quantity that in a unique manner can be associated with the vertex u of graph G. In this paper the exact formula for two types of geometric-arithmetic index of V- phenylenic nanotube are given. Throughout this section G is a simple connected graph with vertex and edge sets V(G) and E(G), respectively. A topological index is a numeric quantity from the structure of a graph which is invariant under automorphisms of the graph under consideration. A topological index is a numeric quantity from the structural graph of a molecule. Usage of topological indices in chemistry began in 1947 when chemist Harold Wiener developed the most widely known topological descriptor, the Wiener index, and used it to determine physical properties of types of alkanes known as paraffin. The concept of geometric-arithmetic indices was introduced in the chemical graph theory. These indices