Recent results on topological indices of nanotubes

Abstract

Topological indices of nanotube? are numerical descriptors that are derived from graph of chemical compounds. Such indices based on the distances in graph are widely used for establishing relationships between the structure of nanotubes and their physico-chemical properties. Harold Wiener in 1947 introduced the notion of path number of a graph as the sum of the distances between two carbon atoms in the molecules, in terms of carbon-carbon bound. The Wiener index of graph G is defined as W(G)= 1/2 ∑u,v∈V(G) d(u,v), where V(G) is the set of vertices of the graph and d(u,v) is the distance between two vertices u,v. The hyper Wiener index of G is defined by WW(G)= 1/2 W(G) +1/4 ∑uv∈V(G) d(u,v)2. In this paper we present some new results on topological indices of nanotubes and calculate hyper Wiener index of some nanotubes. © 2007 American Institute of Physics.