Graph-theoretical applications to chemistry are reviewed from a personal point of view in the context of the gradual acceptance of the value of such applications by the chemical and informational community. Initial problems involved enumerations of isomers that required the use of molecular (constitutional) graphs and techniques such as Polya's theorem, including valence isomers of annulenes, benzenoids, and diamond. hydrocarbons (polymantanes). Problems connected with structural coding and retrieval of chemical information followed. Reaction graphs exemplify a different type of graphs. For QSAR/QSPR studies, global graph invariants (topological indices, TIs) have proved their usefulness; they are based on local vertex invariants (LOVIs) which until recently were exclusively integers, leading to high degeneracy of TIs. Newly introduced real-number LOVIs are briefly reviewed. This retrospective section ends with applications of graph theory (GT) to elemental carbon nets and to fullerenes. Then a few predictions are made for promising developments in the future: increasing use of GT for information processing, development of LOVIs and TIs incorporating stereochemical features, and increased use of TIs for molecular modeling and drug design, along with more sophisticated molecular graphics methods.
