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.