WIENER INDEX AND DETOUR INDEX OF CYCLIC SILICATE NETWORK AND CYCLIC DIAMOND SILICATE NETWORK

摘要

Let G(p,q) be a graph with p vertices and q edges. Let d(u,v) be the distance between two vertices u, v e V(G). The Wiener Polynomial of a graph G is a polynomial in the variable x and is denoted by W(G:x) and is defined as W(G:x) = ∑x~(d(u,v)), where u, v e V(G) and the summation is taken over all unordered distinct pairs of vertices u, v e V(G). The Wiener Index is the first-order differentiation of W(G:x) with respect to x and is defined as WI(G) = W'(G:1). Similar to Wiener Polynomial of a graph, a Detour polynomial is defined as D(G:y) = ∑y~(D(u,v)), where D(u,v) is the detour distance between every unordered distinct pair of vertices u,v e V(G). The Detour Index is the first order differentiation of D(G:y) with respect to y and is defined as DI(G) = D'(G:1). In this paper, based on the above two definitions the Wiener Index and the Detour Index of Cyclic Silicate network and cyclic diamond silicate network are obtained.