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 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. 1

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. 1.

. Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, using an algorithmic version of Burnside's table of marks, computing double coset representatives, and computing Sylow subgroups of automorphism groups can be explained in this way. The exposition is based on graph theoretic concepts to give an easy explanation of data structures for group actions. 1. A General Point of View A natural goal in mathematical theories is a full description of the objects that are investigated. This goal has been successfully achieved in some cases, for example all finite abelian groups and with much more effort all finite simple groups. More often one restricted the research activity firstly to more modest problems like the pure existence of any object with som...