NOTES ON SOME LESS KNOWN EARLY CONTRIBUTIONS TO CHEMICAL GRAPH-THEORY

A dozen less known, but important, contributions to the development an d application of graph theory to chemistry are reviewed. The relevance of these works is pointed out. They include papers which appear to ha ve been known to only a few involved in the recent revival of graph-th eoretical methods in chemistry. Among such papers that have escaped wi der attention are Flavitzky's enumeration of isomers (1874), Muirhead' s work on the comparability of functions (1901) and the review article on graph theory in chemistry by Balandin (1940). A similar class incl udes works by Bloch, who first introduced the nearest neighbour approx imation, well-known from the Huckel molecular orbital calculations; Wh eland, who used the polynomial expansion for enumeration of valence st ructures prior to the well-known Polya's theorem and Sachs, who outlin ed a scheme for enumerating various cycles in a molecule years before more recent schemes have been developed. In addition, we review a work by Heilbronner who reveals an intriguing relationship between valence structures and molecular connectivity and a work by Marcus, concerned with bond-additive properties of molecules, which anticipated much of the recent work on bond indices in benzenoid hydrocarbons and the rol e of circuits in such systems.