1Professor Emeritus, P.G. & Research Department of Mathematics, Bishop Heber College, Tiruchirappalli-17, Tamilnadu, India. Email: kaladevi1956@gmail.com
2Research Scholar, P.G. & Research Department of Mathematics, Bishop Heber College, Tiruchirappalli-17, Tamilnadu, India. Email: selvaranip1002@gmail.com
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 ∈ 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) = Σxd(u,v), where u, v ∈ V(G) and the summation is taken over all unordered distinct pairs of vertices u, v ∈ 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) = ΣyD(u,v), where D(u,v) is the detour distance between every unordered distinct pair of vertices u,v ∈ 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.
Wiener Polynomial, Detour Polynomial, Wiener Index, Detour Index
