Harary Index of Zigzag Polyhex Nanotorus

One of considerable topics in chemistry is surveying the quantitative structure-property relationship between the structure of a molecule and chemical, physical and biological properties of it(QSPR). For this purpose, the form of molecule must be coded according to numbers. A common method, for coding the molecule structure, is to assign a graph to the molecule, where the vertices are atoms of molecule and edges are chemical bonds between the atoms. According to this graph, we can assign various numeral values (topological indices), polynomials, matrices and extra to the molecules which are usually invariant under automorphism of graphs (See [1-3]). A novel topological index for the characterization of chemical graphs, derived from the reciprocal distance matrix and named the Harary index in honor of Professor Frank Harary, has independently been defined by Plavšić et al. [4] and Ivanciuc et al. [5] in 1993. The Harary index and the related indices have shown a modest success in structure-property correlations,[3-8] but the use of these indices in combination with other descriptors appears to be very efficacious in improving the QSPR models[8]. For nanotubes and nanotorus, the big size of corresponding graphs makes the calculations complicated. Diudea [9-13] was the first chemist which considered the problem of computing topological indices of nanostructures. Various topological indices have been calculated for these molecules up to this time [13-22]. In this paper, we represent a calculation for Harary index of G=H [p,q], an zigzag polyhex nanotorus. 6 C