On some solved and unsolved problems of chemical graph theory

The development of several novel graph theoretical concepts and their applications in different branches of chemistry are reviewed. After a few introductory remarks we follow with an outline of selected important graph theoretical invariants, introducing some new results and indicating some open problems. We continue with discussing the problem of graph characterization and construction of graphs of chemical interest, with a particular emphasis on large systems. Finally we consider various problems and difficulties associated with special subgraphs, including subgraphs representing Kekulé valence structures. The paper ends with a brief review of structure-property and structure-activity correlations, the topic which is one of prime motivations for application of graph theory to chemistry.

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