DETOUR SUM AND WIENER SUM OF CHAIN DIAMOND SILICATE NETWORK

摘要

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 ? 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 ? 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 Similarto 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 ? V(G). The Detour sum D(G) = D'(G:1) where denotes ?he first-order differeηtiation 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.