Abstract: Three programs were assessed for their ability to predict mass spectral fragmentation patterns for all constitutional isomers of an experimental low-resolution electron impact mass spectrum (EI-MS), given the molecular formula, and use this information to identify the "correct structure". MOLGEN 3.5 was used to generate the structures, while all spectra were extracted from the NIST database. The commercial programs Mass Frontier and ACD MS Manager, as well as MOLGEN-MSF (developed by the University of Bayreuth) were used to generate mass spectral fragments. MOLGEN-MSF was used to generate "match values" to compare the different programs and their ability to identify the "correct structure". Although high match values could be achieved with certain settings, the ranking of the correct structure relative to other constitutional isomers was not significantly better than the results published previously and in some cases significantly worse. Furthermore, all programs showed bias toward specific structures, which changed significantly with minor changes to the program settings. Thus, advances in mass spectral fragment prediction have not necessarily improved computer aided structure elucidation (CASE) from EI-MS and indicate that caution must be used when confirming the identity of a compound only based on the match between its predicted fragments and the mass spectrum.

Abstract: Structure generation and mass spectral classifiers have been incorporated into a new method to gain further information from low-resolution GC-MS spectra and subsequently assist in the identification of toxic compounds isolated using effect-directed fractionation. The method has been developed for the case where little analytical information other than the mass spectrum is available, common, for example, in effect-directed analysis (EDA), where further interpretation of the mass spectra is necessary to gain additional information about unknown peaks in the chromatogram. Structure generation from a molecular formula alone rapidly leads to enormous numbers of structures; hence reduction of these numbers is necessary to focus identification or confirmation efforts. The mass spectral classifiers and structure generation procedure in the program MOLGEN-MS was enhanced by including additional classifier information available from the NIST05 database and incorporation of post-generation 'filtering criteria'. The presented method can reduce the number of possible structures matching a spectrum by several orders of magnitude, creating much more manageable data sets and increasing the chance of identification. Examples are presented to show how the method can be used to provide 'lines of evidence' for the identity of an unknown compound. This method is an alternative to library search of mass spectra and is especially valuable for unknowns where no clear library match is available.

Abstract: After a few remarks on the history of molecular modelling we describe certain mathematical aspects of the generation of molecular structural formulae. The focus is on the automatic generation of structural formulae for the purpose of molecular structure elucidation and the examination of molecular libraries. The aim is to give a review and to point to relevant literature. We demonstrate an application in the area of quantitative structure-property/activity relationships. Then, we give a glance on ongoing research in the generation of 3D structures (stereoisomers and conformers), and finally we mention two problems that should be solved in the near future, the possible use of hypergraphs, and the generation of patent libraries.

Abstract: A general mathematical description, mostly in terms of graph theory, is given for reactions of organic chemistry. The corresponding computer program generates all products that can result from a given set of starting materials interacting according to a given set of reaction schemes. Example reactions from combinatorial chemistry, synthetic organic chemistry, and mass spectroscopic structure elucidation are considered in detail.

Abstract: y-Randomization is a tool used in validation of QSPR/QSAR models, whereby the performance of the original model in data description (r2) is compared to that of models built for permuted (randomly shuffled) response, based on the original descriptor pool and the original model building procedure. We compared y-randomization and several variants thereof, using original response, permuted response, or random number pseudoresponse and original descriptors or random number pseudodescriptors, in the typical setting of multilinear regression (MLR) with descriptor selection. For each combination of number of observations (compounds), number of descriptors in the final model, and number of descriptors in the pool to select from, computer experiments using the same descriptor selection method result in two different mean highest random r2 values. A lower one is produced by y-randomization or a variant likewise based on the original descriptors, while a higher one is obtained from variants that use random number pseudodescriptors. The difference is due to the intercorrelation of real descriptors in the pool. We propose to compare an original model's r2 to both of these whenever possible. The meaning of the three possible outcomes of such a double test is discussed. Often y-randomization is not available to a potential user of a model, due to the values of all descriptors in the pool for all compounds not being published. In such cases random number experiments as proposed here are still possible. The test was applied to several recently published MLR QSAR equations, and cases of failure were identified. Some progress also is reported toward the aim of obtaining the mean highest r2 of random pseudomodels by calculation rather than by tedious multiple simulations on random number variables.

Abstract: This perspective article provides an assessment of the state-of-the-art in the molecular-resolution analysis of complex organic materials. These materials can be divided into biomolecules in complex mixtures (which are amenable to successful separation into unambiguously defined molecular fractions) and complex nonrepetitive materials (which cannot be purified in the conventional sense because they are even more intricate). Molecular-level analyses of these complex systems critically depend on the integrated use of high-performance separation, high-resolution organic structural spectroscopy and mathematical data treatment. At present, only high-precision frequency-derived data exhibit sufficient resolution to overcome the otherwise common and detrimental effects of intrinsic averaging, which deteriorate spectral resolution to the degree of bulk-level rather than molecular-resolution analysis. High-precision frequency measurements are integral to the two most influential organic structural spectroscopic methods for the investigation of complex materials-NMR spectroscopy (which provides unsurpassed detail on close-range molecular order) and FTICR mass spectrometry (which provides unrivalled resolution)-and they can be translated into isotope-specific molecular-resolution data of unprecedented significance and richness. The quality of this standalone de novo molecular-level resolution data is of unparalleled mechanistic relevance and is sufficient to fundamentally advance our understanding of the structures and functions of complex biomolecular mixtures and nonrepetitive complex materials, such as natural organic matter (NOM), aerosols, and soil, plant and microbial extracts, all of which are currently poorly amenable to meaningful target analysis. The discrete analytical volumetric pixel space that is presently available to describe complex systems (defined by NMR, FT mass spectrometry and separation technologies) is in the range of 10(8-14) voxels, and is therefore capable of providing the necessary detail for a meaningful molecular-level analysis of very complex mixtures. Nonrepetitive complex materials exhibit mass spectral signatures in which the signal intensity often follows the number of chemically feasible isomers. This suggests that even the most strongly resolved FTICR mass spectra of complex materials represent simplified (e.g. isomer-filtered) projections of structural space.

Abstract: Multilinear QSAR models are developed for the largest and most diverse set of PPARgamma agonists treated hitherto. Binding of these small molecules to the human nuclear receptor PPARgamma is described by models that are built on simple 2D molecular descriptors and nevertheless are of good quality and predictive power (e.g., 144 compounds, 10 descriptors, r2=0.79, r2(cv)=0.76). The models presented are thoroughly validated by crossvalidation, randomization experiments, bootstrapping, and training set/test set partitioning. They may therefore be helpful in the design of new antidiabetic drug candidates. For gene transactivation, the functional activity of the agonists, a corresponding model for a similarly diverse compound set is of somewhat lower statistical quality.

Abstract: Two important tasks in computer-aided structure elucidation (CASE) are the generation of candidate structures from a given molecular formula, and the ranking of structure candidates according to compatibility with an experimental spectrum. Candidate ranking with respect to electron impact mass spectra is based on virtual fragmentation of a candidate structure and comparison of the fragments’ isotope distributions against the spectrum of the unknown compound, whence a structure–spectrum compatibility matchvalue is computed. Of special interest is the matchvalue’s ability to distinguish between the correct and false constitutional isomers. Therefore a quality score was computed in the following way: For a (randomly selected) spectrum–structure pair from the NIST MS library all constitutional isomers are generated using the structure generator MOLGEN. For each isomer the matchvalue with respect to the library spectrum is calculated, and isomers are ranked according to their matchvalues. The quality of the ranking can be quantified in terms of the correct structure’s relative ranking position (RRP). This procedure was repeated for 100 randomly selected spectrum–structure pairs belonging to small organic compounds. In this first approach the RRP of the correct isomer was 0.27 on average.

Abstract: The similarity of 608 molecular descriptors (including topological and geometrical indices) is measured using correlation coefficients. The computations are based on a library of 10946 diverse compounds. As a result, the second Zagreb index M_2 and mwc^(3), the molecular walk count of length 3, were found and proven to be affine dependent: mwc^(3) = 2M_2.

Abstract: For molecular weights up to 150, all molecular graphs corresponding to possible organic compounds made of C,H,N,O were generated using the structure generator MOLGEN. The numbers obtained were compared to the numbers of molecular graphs corresponding to actually known compounds as retrieved from the Beilstein file. The results suggest that the overwhelming majority of all organic compounds (even in this low molecular weight range) is unknown. Within the set of C6H6 isomers, a very crude and a highly sophisticated energy content calculation perform amazingly similar in predicting a particular structure’s existence as a known compound.

Abstract: By means of the new software MOLGEN-QSPR, a multilinear regression model for the boiling points of lower fluoroalkanes is established. The model is based exclusively on simple descriptors derived directly from molecular structure and nevertheless describes a broader set of data more precisely than previous attempts that used either more demanding (quantum chemical) descriptors or more demanding (nonlinear) statistical methods such as neural networks. The model's internal consistency was confirmed by leave-one-out cross-validation. The model was used to predict all unknown boiling points of fluorobutanes, and the quality of predictions was estimated by means of comparison with boiling point predictions for fluoropentanes.

Abstract: 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.

Abstract: MOLGEN-QSPR is a software newly developed for use in quantitative structure property relationships (QSPR) work. It allows to import, to manually edit, or to generate chemical structures, to detect duplicate structures, to import or to manually input property values, to calculate the values of a broad pool of molecular descriptors, to establish QSPR equations (models), and using such models to predict unknown property values. In connection with the molecule generator MOLGEN, MOLGEN-QSPR is able to predict property values for all compounds in a predetermined structure space (inverse QSPR). Some of the features of MOLGEN-QSPR are demonstrated on the example of haloalkane boiling points. The data basis used here is broader than in previous studies, and the models established are both more precise and simpler than those previously reported.

Abstract: The MOLGEN Chemical Identifier MOLGEN-CID is a software module freely accessible via the Internet. For a molecule or graph entered in molfile format (2D) it produces, by a canonical renumbering procedure, a canonical molfile and a unique character string that is easily compared by computer to a similar string. The mode of operation of MOLGEN-CID is detailed and visualized with examples.

Abstract: A new software package MOLGEN-QSPR for the exploration of quantitative structure property relationships is introduced. Practical results obtained using this software are presented.

Abstract: MOLGEN is a software package for the fast and redundancy free generation of structural formulae corresponding to prescribed data such as molecular formula, ring sizes, required or forbidden substructures, hydrogen distribution, hybridization etc. A particular version, MOLGEN-COMB, generates combinatorial libraries, starting from a given central molecule. The generation of a library corresponding to a given Markush formula, as encountered in chemistry patents is a quite similar task, and so MOLGEN applies to this problem as well.

Abstract: Artificial neural networks are capable of predicting the C-13 chemical shifts of organic molecules nearly as fast as incremental methods while maintaining the accuracy of database methods. In this article, we apply a recently developed neural network (Meiler et. al., J. Chem. Inf. Comput. Sci. 2000, 40, 1169-1176), to the screening of large sets of molecules obtained by structure generators in the process of automated structure elucidation. Specifically, we apply the network to sets of structures generated by MOLGEN (Benecke et. al., Anal. Chim. Acta 1995, 314, 141-147) for ten randomly selected molecules of less than 13 non-hydrogen atoms. The computed C-13 NMR spectra are compared to the experimental spectrum; in all cases, the computed spectrum belonging to the example molecule yields a significantly smaller deviation to the experimental data then all other predicted spectra. This result suggests that the approach is suitable for automated structure prediction for organic molecules with up to 12 non-hydrogen atoms.

Abstract: The limits of a recently proposed computer method for finding all distinct substructures of a chemical structure are systematically explored within comprehensive graph samples which serve as supersets of the graphs corresponding to saturated hydrocarbons, both acyclic (up to n = 20) and (poly)cyclic (up to n = 10). Several pairs of smallest graphs and compounds are identified that cannot be distinguished using selected combinations of invariants such as combinations of Balaban's index J and graph matrix eigenvalues. As the most important result, it can now be stated that the computer program NIMSG, using J and distance eigenvalues, is safe within the domain of mono- through tetracyclic saturated hydrocarbon substructures up to n = 10 (oligocyclic decanes) and of all acyclic alkane substructures up to n = 19 (nonadecanes), i.e., it will not miss any of these substructures. For the regions surrounding this safe domain, upper limits are found for the numbers of substructures that may be lost in the worst case, and these are low. This taken together means that the computer program can be reasonably employed in chemistry whenever one is interested in finding the saturated hydrocarbon substructures. As to unsaturated and heteroatom containing substructures, there are reasons to conjecture that the method's resolving power for them is similar.

Abstract: Most graphs and most 4-graphs are nonplanar, whereas most compounds of Organic Chemistry are gt-planar. This potentially useful fundamental difference between graphs and compounds was empirically obtained by testing for gt-planarity representative graphs and all compounds in the Beilstein file. The Beilstein search did uncover compounds whose gt-nonplanarity was hitherto unknown. gt-Nonplanar peptides/proteins were retrieved from the CAS Registry file.

Abstract: We briefly describe a project devoted to the implementation of the software package MOLGEN-COMB for the simulation of combinatorial chemistry and the optimization of its experiments.

Abstract: The construction of complete lists of regular graphs up to isomorphism is one of the oldest problems in constructive combinatorics. In this article an efficient algorithm to generate regular graphs with a given number of vertices and vertex degree is introduced. The method is based on orderly generation refined by criteria to avoid isomorphism checking and combined with a fast test for canonicity. The implementation allows computing even large classes of graphs, like construction of the 4-regular graphs on 18 vertices and, for the first time, the 5-regular graphs on 16 vertices. Also in cases with given girth, some remarkable results are obtained. For instance, the 5-regular graphs with girth 5 and minimal number of vertices were generated in less than 1 h. There exist exactly four (5, 5)-cages.

Abstract:

Abstract:

Abstract:

Abstract: In this note we give the smallest 4-regular 4-chromatic graphs with girth 5. There are exactly one on 21 vertices and one on 25 vertices.

Abstract: Chemical structure enumeration and sampling have been studied by mathematicians, computer scientists, and chemists for quite a long time. Given a molecular formula plus optionally a list of structural constraints, the typical questions are: (1) How many isomers do exist? (2) What are their structures like? And, especially if (2) cannot be answered completely: (3) How to get a sample?<br> In this chapter we describe algorithms for answering these questions. The techniques are based on representation of chemical compounds as molecular graphs, i.e. they are mainly applied to constitutional isomers, with a few extensions to stereoisomers. The major problem is that in silico molecular graphs have to be represented as labeled structures, while the atoms in real chemical compounds are not labeled. The mathematical concept for approaching this problem is to consider orbits of labeled molecular graphs under the operation of the given symmetry group. We have to solve the so-called 'isomorphism problem'.<br> According to our introductory questions, we distinguish three disciplines: Counting, enumeration and sampling. Counting means that only the number of structures is calculated, while the structures themselves are not produced by the algorithm. Counting methods are mainly based on Polya's theory. Typical applications are permutational isomers and acyclic compounds. In contrast to counting, generating structures means that each structure is constructed by the algorithm and can be written to the output. When generating structures we further distinguish deterministic and stochastic approaches. Deterministic structure generators solve the problem exhaustively and without redundance.<br> First structure generators of this type were developed in the late 1960s. As part of the DENDRAL project a generator for acyclic graphs was developed which was later extended to handle cyclic structures as well. With Read's orderly generation a new principle was discovered, which lead to new types of structure generators. These were able to enumerate huge lists of isomers at a speed of several thousand structures per second. Especially applications in structure elucidation required to handle long lists of constraints efficiently with the objective to generate only small numbers of structures. In this context fast isomorphism tests lost importance, so that the enumeration of the labeled structures became the bottleneck. A quite new principle that meets these demands is called constrained generation.<br> Sometimes we face situations when deterministic generation is either impossible or simply not required. Then structure sampling provides an alternative. There are methods available for uniformly distributed sampling of graphs and molecular graphs. Stochastic structure generators following the principles of simulated annealing and genetic programming are able to tackle certain problems that are out of reach for deterministic generators.<br> Beyond generation of isomers, the described methods can be applied to generate extensive parts of the chemical space or to enumerate combinatorial libraries. We outline the adaptations in algorithms required for these purposes.

Abstract: The generation of molecular graphs by computer programs has undergone some changes. The development is reported with focus on various mathematical methods that are created and employed in this process. No attempt has been made to explicitely state and prove the theorems but this overview contains hints to the relevant literature. In particular, a new generator MOLGEN 4.0 is described that aims at highest flexibility in using constraints during the generation process and, thus, meeting the needs of practical applications.

Abstract: Some of the mathematical methods will be described which are implemented in the software package MOLCOMB that allows to simulate combinatorial chemistry by generating combinatorial libraries and to do some screening according to geometric substructures.

Abstract: The generation of discrete structures up to isomorphism is interesting as well for theoretical as for practical purposes. Mathematicians want to look at and analyse structures and for example chemical industry uses mathematical generators of isomers for structure elucidation. The example chosen in this paper for explaining general generation methods is a relatively far reaching and fast graph generator which should serve as a basis for the next more powerful version of MOLGEN, our generator of chemical isomers.

Abstract: In this paper, we present first results of a new straylight correction algorithm for SCIAMACHY, to be implemented in the operational Level 0-to-l processing software. A re-analysis of the on-ground calibration data (Calibration Keydata) is currently on-going at SRON. We present interesting graphical results from this reanalysis activity, and show the improvement of the new straylight Keydata, coupled to a new straylight correction algorithm, on atmospheric spectra measured with the SCIAMACHY instrument.

Abstract: Most of the computer programs used for automatic spectra interpretation depend on large spectral databases. The experimental spectrum in question is compared with the entries of the database and the structures of the most similar spectra are given as possible solutions. This method has several limitations: (a) The quality of the database spectra restricts the performance; even good experimental spectra may lead to wrong results if the reference spectra are erroneous. (b) If the spectrum of a query substance is not included in the library a reasonable result can only be expected if structures are in the database that are very similar to the unknown and are found be the applied spectral similarity criterion.

Abstract: Mathematische Modelle bilden eine unentbehrliche Grundlage in nahezu allen Bereichen von Wissenschaft und Technik. Immer häufiger werden auch Problemstellungen der organischen Chemie durch mathematische Modellierung simuliert und gelöst.<br> Motivation ist dabei oft die Suche nach neuen Wirkstoffen und Materialien mit angestrebten biologisch-pharmazeutischen oder physiko-chemischen Eigenschaften. Wurde eine entsprechende Verbindung synthetisiert und gefunden, besteht eine weitere wichtige Aufgabe darin, die molekulare Struktur der oft noch unbekannten Substanz zu bestimmen. Zu diesen Zweck verwendet man hauptsächlich spezielle physiko-chemische Eigenschaften, die aus spektroskopischen Methoden gewonnen werden.<br> Bei der Suche nach neuen Wirkstoffen und Materialien finden immer häufiger Techniken der kombinatorischen Chemie Verwendung. Dabei werden aus mehreren Sätzen chemischer Bausteine sämtliche Kombinationen synthetisiert und anschließend auf ihre biologisch-pharmazeutische Wirksamkeit getestet oder hinsichtlich angestrebter physiko-chemischer Eigenschaften untersucht. Der enorme Vorteil dieser Methode besteht darin, dass sowohl die Synthese als auch das Screening in hohem Maße automatisiert und parallelisiert werden kann. Obwohl somit erstaunliche Durchsatzraten erzielt werden, mahnen Kosten- und Zeitgründe zur gewissenhaften Planung und zur automatischen Auswertung derartiger Experimente.<br> Die Optimierung kombinatorisch-chemischer Experimente und die automatisierte molekulare Strukturbestimmung werfen vielfältige Probleme auf, die nach mathematischer Modellierung mit Hilfe von algebraisch-kombinatorischen Konstruktionsalgorithmen, graphentheoretischen Invarianten und statistischen Lernverfahren gelöst werden können. Die entscheidenden Problemstellungen betreffen die <ul> <li> Strukturgenerierung:<br> In der kombinatorischen Chemie benötigt man Methoden, um virtuelle kombinatorische Bibliotheken zu konstruieren. Meist werden solche Strukturräume durch Reaktanden und Reaktionen definiert. In dieser Arbeit werden Algorithmen zur reaktionsbasierten Strukturgenerierung beschrieben.<br> Für die molekulare Strukturaufklärung werden Algorithmen verwendet, die ausgehend von der Bruttoformel eines Analyten unter Berücksichtigung struktureller Restriktionen mögliche Strukturformeln generieren können. Strategien zur bruttoformelbasierten Strukturgenerierung werden vorgestellt.<br> Wichtige Methoden für beide Problemkreise bilden kanonische Nummerierung und ordnungstreue Erzeugung. </li> <li> Suche nach Beziehungen zwischen Struktur und Eigenschaft:<br> Um Eigenschaften für die Strukturen virtueller kombinatorischer Bibliotheken vorhersagen zu können, verwendet man quantitative Struktur-Eigenschafts-Beziehungen (QSPR). Diese werden zuvor anhand einer tatsächlich synthetisierten und gescreenten kleineren realen Bibliothek ermittelt.<br> Die computer-unterstützte molekulare Strukturaufklärung (CASE) verfolgt das Ziel, ausgehend von spektroskopisch gemessenen Eigenschaften einer unbekannten chemischen Verbindung ihre molekulare Struktur zu bestimmen.<br> Die mathematischen Werkzeuge für diese Aufgaben sind molekulare bzw. spektrale Deskriptoren und statistische Lernverfahren. </li> </ul> Im ersten Teil der Arbeit werden die benötigten Modelle und Methoden beschrieben: Die Darstellung von chemischen Verbindungen, molekularen Substrukturen und chemischen Reaktionen, ordnungstreue und zielgerichtete Erzeugung zur bruttoformelbasierten Strukturgenerierung, Kernstruktur-Ligand-Anlagerungen und Konstruktion nach dem Netzwerkprinzip für die reaktionsbasierte Strukturgenerierung. Auf Seiten des überwachten statistischen Lernens werden Klassifikation und Regression durch lineare Modelle, künstliche neuronale Netze, Support-Vektor-Maschinen, Entscheidungsbäume und k-nächste Nachbarn vorgestellt.<br> Der zweite Teil enthält konkrete Anwendungen zu Problemstellungen aus der Chemie: Kombinatorische Bibliotheken werden generiert, z.B. nach Ugis Siebenkomponentenreaktion. Mit Hilfe von verschiedenen molekularen Deskriptoren (arithmetische, topologische und geometrische Indizes, Substruktur-Vielfachheiten) und statistischen Lernverfahren werden QSPR bestimmt, verglichen und zur Vorhersage herangezogen. Problemstellungen sind dabei Siedepunkte von Decanen, physikalische Dichten von Propylacrylaten und die antibakterielle Aktivität von Quinolonen. Die Untersuchungen zur CASE zielen auf die Interpretation und Verifikation von Massenspektren. Rankingfunktionen für Brutto- und Strukturformeln werden definiert und getestet. Verschiedene Klassifikationsverfahren zur Bestimmung von MS-Klassifikatoren werden verglichen. Weiterführende Studien untersuchen u.a. die Möglichkeiten hochauflösender MS.

Abstract: Die Erzeugung vollständiger Listen nichtisomorpher regulärer Graphen gehört zu den ältesten Problemen der konstruktiven Kombinatorik. Bereits gegen Ende des letzten Jahrhunderts wurden Versuche unternommen, vollständige Listen 3-regulärer Graphen zu gegebener Knotenzahl aufzustellen. So gelang es Jan de Vries im Jahre 1889 alle 3-regulären Graphen mit 10 Knoten anzugeben. Mit der Entwicklung leistungsfähiger Rechner wurden auch auf diesem Gebiet entscheidende Fortschritte erzielt.<br> Die vorliegende Arbeit beschreibt einen Algorithmus zur Erzeugung der k-regulären Graphen mit n Knoten zu gegebenem k und n. Ausgangspunkt dafür war ein Verfahren zur Konstruktion 3-regulärer Graphen, das Gunnar Brinkmann in 'Generating cubic graphs faster than isomorphism checking' vorstellt. Um auch für größeren Grad eine hohe Effizienz zu erreichen, verwende ich zudem Techniken, die sich schon in dem bestehenden MOLGEN - Generator bewährt haben.<br> Auf Grundlage dieser Methoden wurde ein Generator entwickelt, mit dem auch große Probleme in vertretbarer Zeit abgearbeitet werden können, so etwa die Konstruktion der 4-regulären Graphen mit 18 Knoten und der 5-regulären Graphen mit 16 Knoten. Es besteht zudem die Möglichkeit eine untere Grenze für die Taillenweite der erzeugten Graphen vorzuschreiben (auf der Titelseite ist ein 3-regulärer Graph mit 36 Knoten und Taillenweite 8 abgebildet). Auch mit dieser Restriktion werden bemerkenswerte Resultate erzielt. So wurden beispielsweise alle vier (5,5)-Cages berechnet. Damit ist dieses Problem vollständig gelöst.

Abstract: In den letzten Jahren sind in der Chemie ganz neue Methoden der Massensynthese1 entwickelt worden, die mittlerweile ins Zentrum des Interesses und der Diskussion gerückt sind. Sie werden u.a. im pharmazeutischen Bereich und in den Materialwissenschaften angewendet und unter der Überschrift kombinatorische Chemie zusammengefaßt. Es geht dabei um die durch Roboter unterstützte und gesteuerte Erzeugung von Hunderten oder gar Tausenden chemischer Substanzen "auf einen Schlag". Schon der Name kombinatorische Chemie läßt Mathematiker und Informatiker aufhorchen. Er zeigt deutlich, daß begleitende mathematisch-kombinatorische Überlegungen im Vorfeld solcher Experimente von Nutzen sein sollten. Da es sich dabei um Massensynthese handelt, sieht der Informatiker sofort, daß bei Experimenten der kombinatorischen Chemie eine riesige Datenflut anfallen wird, die es zu strukturieren gilt. Wir wollen deshalb hier unsere Erfahrungen schildern, die wir im Rahmen zweier Projekte gemacht haben, und wir werden einige der Probleme aufzeigen, die wir in diesem Zusammenhang lösen wollen. Es handelt sich dabei um ein DFG-Projekt zur Materialforschung (gemeinsam mit Prof. Ziegler, FAN) von Precursorkeramiken, und ein BMBF-Projekt (Federführung Fa. Henkel) zur Optimierung und Analyse solcher Verfahren.