The Rich Legacy of Half a Century of the Wiener Index

During the years 1947-1948 Harry Wiener published a series of five papers that introduced into chemistry two novel graph-theoretical invariants. These invariants were specifically designed to characterize alkane molecules and he termed them the polarity number and the path number. The latter number is nowadays more commonly referred to as the Wiener topological index. Our focus here will be primarily on this index and its remarkable historical development over the past half century. We first outline its origins and then discuss its extensive applications and elaboration down to the present time with especial focus on the first thirty years. Our chapter serves to document the fact that Wiener's seminal work has spawned much creative research activity within the broad domain of chemistry. The Wiener index was the first of the current plethora of topological indices that now number in the hundreds. The prolific production of such indices over the years can be ascribed to the fecundity of Wiener's ideas in the stimulation of new scientific endeavors. In this chapter it is our intention not only to chronicle but also to celebrate the rich legacy of Wiener's pioneering contributions to chemistry.