TOPOLOGICAL INDEX OF VPH (m,n) NANOTORUS

Suppose that G be molecular graph the vertex and edge-sets of which are represented by V(G) and E(G), respectively. A topological index of a graph G is a numeric quantity related to G. The oldest topological index is the Wiener index. Numerous of its chemical applications were reported and its mathematical properties are well understood. In Rrefs [5-9] the authors defined a new topological index and named it Padmakar-Ivan index. They abbreviated this new topological index as PI. This newly proposed topological index does not coincide with the Wiener index for acyclic molecules. The Szeged index is another topological index which is introduced by Ivan Gutman. To define the Szeged index of a graph G, we assume that e = uv is an edge connecting the vertices u and v. Suppose Nu(e|G) is the number of vertices of G lying closer to u and Nv(e|G) is the number of vertices of G lying closer to v. Edges equidistance from u and v are not taken into account. Then the Szeged index of the graph G is defined as Sz(G) = ∑e=uv∈E(G)Nu(e|G)Nv(e|G), see also Ref [14]. In Refs. [15-20] the PI and Szeged indices of some hexagonal graphs containing nanotubes and nanotorus are computed. In this paper, we continue this work to compute the Szeged index of Vphenylenic VPH[m,n] nanotorous . Our notation is standard and mainly taken from Refs [21, 22].