Wiener index of graphs with more than one cut-vertex Original Research Article

For a simple connected undirected graph GG, the Wiener indexW(G)W(G) is defined as half the sum of all distances of the form d(u,v)d(u,v), where the summation is over all possible vertex pairs u,vu,v in GG. Assuming that GG has more than one cut-vertex, we obtain an expression for W(G)W(G) in terms of the Wiener indices of the blocks of GG and other quantities.