On the Wiener index of trees from certain families

The Wiener index W( G) of a connected graph G is the sum of the distances d( u, v) between all pairs of vertices u and v of G. This index seems to have been introduced in [22] where it was shown that certain physical properties of various paraffin species are correlated with the Wiener index of the tree determined by the carbon atoms of the corresponding molecules. Canfield, Robinson, and Rouvray [1] described a recursive procedure for determining the Wiener index of a tree and gave an extensive list of papers involving chemical applications of the index; see also [18] for an expository account of work in this area. More recently, McKay, and also Merris (see e.g. [10], [11], or [14]), have