PUB - Publikationen an der Universität Bielefeld

In this text, constructive definitions of several classes of cubic maps, as well as methods to avoid constructing pairwise isomorphic maps are given. In the first part, inductive definitions of all simple cubic toroidal maps, as well as of those simple cubic toroidal maps containing only triangles, squares, pentagons, hexagons, and heptagons, are given. In the second part, an algorithm for the construction of restricted classes of cubic maps is presented. The restrictions are to be given by the user. The user can determine the genus of the maps in the class, the vertex number and the permitted faces. Moreover, the user can give further restrictions concerning connectivity and simpleness or incidence relationships between faces of certain degrees. To every definition and algorithm, there exists a corresponding computer program which can be used to actually construct the class of maps. The computer programs are described in the appendix.