Relation between Wiener-type topological indices of benzenoid molecules

The distance d(u,v|G) between the vertices u and v of a molecular graph G is the length of a shortest u,v-path. We consider a class of Wiener-type topological indices Wλ(G), defined as the sum of the terms d(u,v|G)λ over all pairs of vertices of G. Several special cases of Wλ(G), namely for λ=+1 (the original Wiener number) as well as for λ=−2,−1, +1/2, +2 and +3, were previously studied in the chemical literature, and found applications as molecular structure-descriptors. We establish a relation between Wλ+1 and Wλ, applicable for benzenoid molecules, phenylenes, chemical trees, and other types of molecular graphs.