Journal of M olecular Structure (Theochem), 227 (1991) 17-42 Elsevier Science Publishers B.V., Amsterdam 17 zyxwvuts CHEMICAL AND REACTION METRICS FOR GRAPH- THEORETICAL MODEL OF ORGANIC CHEMISTRY* V. KVASNICKA and J. POSPICHAL Department of Mathematics, Slovak Technical University, 81237 Bratislava (Czechoslovakia) (Received 22 September 1989; in final form 20 March 1990) ABSTRACT Two different metrics for families of isomeric molecular graphs are determined. The chemical distance between a pair of molecular graphs corresponds to the number of edges that should be created and/or annihilated in the course of chemical transformation of the given graph into an- other one. The reaction distance is determined as the minimal number of so-called elementary transformations (simple heterolytic dissociations and associations) that are necessary for the transformation of the initial molecular graph into the product molecular graph. The chemical transformations are formally expressed by the reaction graphs. Two approaches for the construc- tion of reaction networks are suggested. The first approach consists of successive applications of prototype reaction graphs into the initial molecular graph. The second approach is based on the decomposition of the reaction graph into prototype reaction graphs. Both these approaches are substantially accelerated by heuristic rules which manifest the well-known organic chemistry principle of minimal structural change. INTRODUCTION The graph-theoretical model [l-6] of organic chemistry offers very simple, yet sufficiently diverse, formal tools for the description of chemical structures and reactions [ 71. A similar idea was first conceived by Ugi and Dugundji [ 8,9] in the framework of their famous matrix model of constitutional chemistry. The graph-theoretical model can, loosely speaking, be understood as an alter- native formulation of this matrix model; instead of matrices it employs the notions and concepts of graph theory. Moreover, this transfer from matrices to graphs allows the use of the very rich and flexible formal tools of graph theory. Accordingly, many theoretical and algorithmic problems of the model can be formulated and considered by making use of the theoretical machinery of graph theory. In particular, two different graph metrics (chemical and re- action distance) can be introduced in a straightforward way, whereas their inclusion in the matrix model may give rise to many obstacles and pitfalls. The *Dedicated to Professor Rudolph Zahradnfk. 0166-1280/91/$03.50 0 1991- Elsevier Science Publishers B.V.