Graph Theory and Chemistry

WilR76 Wilson, R. J. Graph theory and chemistry. Colloq. Math. Soc. Janos Bolyai (1976) 1147-1164. 

Balaban, A.T. and Harary, F. (1976). Early History of the Interplay Between Graph Theory and Chemistry. In Chemical Applications of Graph Theory (Balaban, A.T., ed.). Academic Press, London (UK), pp. 1-4. 

Schultz, H. P., Schultz, E. B., Schultz, T. P. Topological organic chemistry. 9. Graph theory and molecular topological indices of stereoisomeric organic compounds. J. Chem. Inf. Comput. Sci. 1995, 35, 864-870. 

King, B. (1993) Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry (CRC Press Boca Raton, Ann Arbor). 

Johnson, M. (1985) Relating metrics, lines, and variables defined on graphs to problems in medicinal chemistry. In Graph theory and its applications to algorithms and computer science, Alavi, Y., et al. (eds.), John Wiley Sons, New York, pp. 457-470. 

HeBr87] W. C. Herndon and A. J. Bruce, Perimeter code for benzenoid aromatic hydrocarbons, in Graph Theory and Topology in Chemistry, ed. by R. B. King and D. H. Rouvray, Studies in Physical and Theoretical Chemistry 51 (1987) 491-513. 

Another application of graph theory to chemistry is in chromosome analysis. Suppose a chromosome is broken into a number of pieces and each piece analyzed. If this is done a number of times, the pieces found will overlap in various ways. 

Balasubramanian, K., Integration of Graph Theory and Quantum Chemistry for Structure-Activity Relationships. SAR QSAR Environ. Res., 1994 2, 59-77. 

Hanson, M. and D. Rouvray. 1987. The Use of Topological Indices to Estimate the Melting Points of Organic Molecules. In Graph Theory and Topology in Chemistry, King, R., Rouvray, D., Eds. Elsevier, Amsterdam, 201. 

Klein DJ (1982) J. Chem. Phys. 77 3098 Klein DJ, Alexander SA (1987) In KingRB, RouvrayDH (eds) Graph theory and topology in chemistry, Elsevier, Amsterdam, pp 404-419... 

The K enumeration of rectangles was the topic for one of the contributions at an International Conference on Graph Theory and Topology in Chemistry, Athens, Georgia, USA, 16-20 March 1987 [22]. Finally we mention that the research area in question has been summarized in details and supplemented in the book of Cyvin and Gutman [2]. Some of the latest developments [21] are not included therein. The present review provides a new twist of the presentation, which is supposed to be suited as an introduction to the fairly complicated analyses of this topic. Because of space limitations we have mainly confined the present contribution to the classes of oblate... 

The revival of interest in the applications of graph theory to chemistry and physics led to the use of already known techniques in mathematics to problems of chemical and physical interests. Two texts appeared on these developments [22,23] in addition to an early book edited by Balaban [24]. 

To repeat the route of chemistry in the kinetic aspect , that was the formulation of the problem. To our mind, however, in the 1930s "the rational classification principle , whose appearance was predicted by Semenov, could not be realized. The possibility of solving this problem appeared only in recent times in terms of the concepts of the graph theory and the qualitative theory of differential equations. The analysis of the effect of the mechanism structure on the kinetic regularities of catalytic reactions is one of the connecting subjects in the present study. 

Simon, J. Proc. Symp. Appl. Math. 1992,45, 97. Simon, J. A Topological Approach to the Stereochemistry ofNonrigid Molecules, in King, R. B. Rouvray, D. H. Eds., Graph Theory and Topology in Chemistry, Elsevier Amsterdam, 1987, pp. 43-75. 

In Table 11, we provide a compilation of books in the rapidly expanding field of computer-aided molecular design and also books on QSAR. Finally, Table 12 lists books on the narrow, well-defined topic of graph theory in chemistry. 

Paul G. Mezey and Nenad Trinajstic, Applied Graph Theory and Discrete Mathematics in Chemistry. Proceedings of the Symposium in Honor of Professor Frank Harary on His 70th Birthday, Saskatoon, Canada, 12-14 September 1991, inJ. Math. Chem., 12 (1-4), Baltzer, Basel, 1993. 

In a follow-on report, it will be shown that affixes are useful in any domain that can not be uniquely described by graph theory and/or measure theory. In the case of chemistry, this occurs for enantiomers. 

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