Detour sum and wiener sum of chain diamond silicate network

Let G(p,q) be a graph with p vertices and q edges. Let d(u,v) denote the distance between two vertices u, v ε V(G). The Wiener Polynomial of a graph G with q edges is denoted by W(G:q) and is defined as W(G, q) = ∑q^d(u,v), where u, v ε V(G) and the sum is taken over all unordered distinct pairs of vertices u,v in V(G). The relation between Wiener Polynomial and Wiener Index is W(G) = W′(G: 1) where ′ denotes the first-order differentiation of W(G:q) with respect to q. Similar to Wiener Polynomial of a graph, a Detour polynomial is defined as D(G:q) = ∑q^D(u,v), where D(u,v) is the detour distance between every unordered distinct pair of vertices u,v ε V(G). The Detour sum D(G) = D′(G: 1) where ′ denotes the first-order differentiation of D(G:q) with respect to q. In this paper, based on the above two definitions the Wiener Polynomial and the Detour polynomial of CHDS(n) is obtained.