Wiener and Schultz Molecular Topological Indices of Graphs with Specified Cut Edges

Let G be a simple, undirected and connected graph. The Wiener index W(G) of G is defined,c to be the sum of distances between all pair of vertices of G, that is, 1/2 Sigma(n)(i=1)Sigma(n)(j=1) d(G)(i,j). The Schultz molecular topological index of G, denoted by MTI(G), is defined to be the summation Sigma(n)(i=1)Sigma(n)(j=1) d(G)(i) (A(ij) + d(G) (i, j)), where n is the order of G, d(G)(i) is the degree of vertex i in G, and d(G)(i, j) is the distance between vertices i and j and A(ij) is the (i, j) - th entry of the adjacency matrix A of G. Denote by G(n,k) the set of graphs with n vertices and k cut edges. In this note, we determine resp. the minimal elements with respect to W(G) and MTI(G) among all elements G in G(n,k)(1 <= k <= n - 3).