A computer package is being developed at Bayreuth for the generation and investigation of discrete structures. The package is a C and C++ class library of powerful algorithms endowed with graphical interface modules. Standard applications can be run automatically whereas research projects mostly require small C or C++ programs. The basic philosophy behind the system is to transform problems into standard problems of e.g. group theory, graph theory, linear algebra, graphics, or databases and then to use highly specialized routines from that field to tackle the problems. The transformations required often follow the same principles especially in the case of generation and isomorphism testing.

Computer Chemistry is of quickly increasing importance, in particular since the flood of data is rapidly growing with the introduction of Combinatorial Chemistry using methods of synthesis in large quantities (libraries) and high throughput screening. The accompanying software that allows to optimize such experiments in advance and to economize the cost of measurement afterwards uses in particular mathematical models of molecules and their description. Such models will be described here and the present state of the generation of molecular models in the computer will be discussed, from the mathematical point of view. A brief description of several applications is given. 1

MOLGEN is a computer program system which is designed for generating molecular graphs fast, redundancy free and exhaustively. In the present paper we describe its basic features, new features of the current release MOLGEN 3.5, and future developments which provide considerable improvements and extensions. 1 Introduction MOLGEN [1--7] is a generator for molecular graphs (=connectivity isomers or constitutional formulae) allowing to generate all isomers that correspond to a given molecular formula and (optional) further conditions like prescribed and forbidden substructures, ring sizes etc. The input consists of ffl the empirical formula, together with ffl an optional list of macroatoms, which means prescribed substructures that must not overlap, ffl an optional goodlist, that consists of prescribed substructures which may overlap, ffl an optional badlist, containing forbidden substructures, ffl an optional interval for the minimal and maximal size of rings, ffl an optional num...

The aim is a description of discrete mathematics used in a project devoted to the implementation of a software package for the simulation of combinatorial chemistry.

Some simple 7-designs with small parameters are constructed with the aid of a computer. The smallest parameter set found is 7-(24; 8; 4): An automorphism group is prescribed for finding the designs and used for determining the isomorphism types. Further designs are derived from these designs by known construction processes.