ON THE DISTANCE-BASED TOPOLOGICAL INDICES OF FULLERENE AND FULLERENYL ANIONS HAVING DENDRIMER UNITS

A topological index is a real number related to a structural graph of a molecule. It does not depend on the labeling or pictorial representation of a graph. In recent years there has been considerable interest in the general problem of determining topological indices of nanotubes, nanotori and fullerenes. It has been established, for example, that the Wiener and hyper-Wiener indices of polyhex nanotubes and tori are computable from the molecular graph of these structures. Accordingly, some of the interest has been focused on computing topological indices of these nanostructures. Let G be an undirected connected graph without loops or multiple edges, with the vertex set V(G) and the edge set E(G). The distance between two vertices x and y is denoted by d(x,y). The Winer index W(G) of G, which is the oldest topological index, is a distance based topological index and is defined as the sum of distances between all vertices of the graph: