In information processing, in combinatorial chemistry, in structure elucidation, and in several other fields of chemistry, the computer-aided generation of all structures (constitutional formulae) within a defined structure space has become increasingly important. In this brief review the mathematical foundations of the classical molecular model and thus of the generation process are outlined, and the current state of structure generation as applied in software developed by the Bayreuth group is discussed.

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Coset algebraic theory developed by Fujita (Shinsaku Fujita, Symmetry and Combinatorial Enumeration in Chemistry, Springer-Verlag, Berlin Heidelberg (1991)) is studied by using (colored) graphs to model coset representations, marks, characters, and group subductions.

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An improved version of a peak assignment algorithm for two-dimensional NMR correlation spectra of zeolites is described. Both the zeolite framework structure and the two-dimensional NMR correlation spectrum can be expressed as graphs such that the task of peak assignment is to find labelings of the vertices of the graphs which show that the two graphs are homomorphic. In this paper, it is shown that an initial analysis of the structure and spectrum graphs provides information about the possible identities of the peaks which can lead to large gains in the efficiency of the peak assignment algorithm. The improvements in the algorithm are demonstrated for the peak assignment of solid state magic-angle spinning ²⁹Si NMR spectra of the purely siliceous zeolite ZSM-5 from two-dimensional ²⁹Si INADEQUATE NMR spectra.

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Let T be an n-vertex tree and e its edge. By n₁(e|T) and n₂(e|T) are denoted the number of vertices of T lying on the two sides of e; n₁(e|T) + n₂(e|T) = n. Conventionally, n₁(e|T) ≤ n₂(e|T). If T^′ and T^′′ are two trees with the same number n of vertices, and if their edges e₁^′,e₂^′,&ldots;,e_n-1^′ and e₁^′′,e₂^′′,&ldots;,e_n-1^′′ can be labelled so that n₁(e_i^′|T^′) = n₁(e_i^′′|T^′′) holds for all i=1,2,&ldots;,n–1, then T^′ and T^′′ are said to be equiseparable. Several previously studied molecular–graph–based structure–descriptors have equal values for equiseparable trees, which is a disadvantageous property of these descriptors. In earlier works large families of equiseparable trees have been found. We now show that equiseparability is ubiquitous, and that almost all trees have an equiseparable mate. The same is true for chemical trees.

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Topicity terms for stereochemical relationships (homotopic, enantiotopic, diastereotopic, etc.) and topicity terms for stereochemical attributes (chirotopic and achiotopic) have been combined to discuss the stereochemistry of tetrahedral molecules. Stereochemical discussions due to such combined usage have exhibited complicated features that would cause misunderstanding or confusion. On the other hand, Sphericity terms (homospheric, enantiospheric, and hemispheric), which are based on orbits of ligands (or other objects), have been clarified to provide us with a simpler terminology for such stereochemical discussions. Sphericity indices have been defined and applied to examining the existence of derivatives.

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