HYPER WIENER INDEX C4C8(S) NANOTORUS

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. Topological indices are one of the descriptors of molecules that play an important role in structure property and structure activity studies, particularly when multivariate regression analysis, artificial neural networks, and pattern recognition are used as statistical tools. One of the topics of continuing interest in structureproperty studies is to arrive at simple correlations between the selected properties and the molecular structure [3, 16]. The hyper Wiener index is one of the recently conceived distancebased graph invariants, used as a structure-descriptor for predicting physicochemical properties of organic compounds. This topological index was introduced by Randi'c and has been extensively studied [10, 13]. Let be a connected graph, the set of vertices and edges of will be denoted by V(G) and E(G), respectively. If e is an edge of G connecting the vertices i and j of G, then we write e = ij. The distance between a pair of vertices i and j of G is denoted by d(i , j). The hyper Wiener index of the graph G is the half sum of distances and square distances over all its vertex pairs (i , j): G