The Eccentric Connectivity and Balaban Indices of an Infinite Family of Nanotorus

Let G=(V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges. For u \inV(G), defined d(u) be degree of vertex u. The eccentricity connectivity index of a molecular graph G is defined as {\Xi} ^{c} (G) = \sum _{u \in V(G)} deg_G (u). ecc(u) , where ecc(u) is defined as the length of u maximal path connecting a to another vertex of G. The Balaban index of a graph G is defined as J(G)= \frac {m}{\mu + 1} \sum _{e=uv} [ d(u) d(v) ]^{- 0.5} , where m is the number of edges of G,  \mu is the cyclomatic number of G and for every vertex x of G, d(x) is the summation of distances between x and all vertices of G. In this paper, we computing eccentricity connectivity and balaban indices for linear polycene parallelogram graph of benzenoid by a new method.