A Collective Property of Trees and Chemical Trees

Abstract

The Wiener index ( W ) and the Hosoya polynomial ( H ) have been calculated for all trees (and thus for all chemical trees) with 20 and fewer vertices. Corroborating an earlier observation (Razinger, M. et al. J. Chem. Inf. Comput. Sci. 1985, 25, 23−27), we show that the ability of W to distinguish between nonisomorphic n -vertex trees (respectively, chemical trees) depends on n in an alternating manner: it increases for even values of n and decreases for odd values of n . An analogous behavior is also found in the case of H .