Generating all planar 0-,1-,2-,3-connected graphs

Abstract

A graph grammar is given which generates all k- connected planar graphs for given k=0,1,2,3; n=# of vertices, m=# of edges, and (for k=0) p=# of components. The method is based on two elementary operations, namely (1) Joining two nonadjacent vertices by an edge, and (2) Replacing a vertex by two adjacent vertices. The operations are applied to plane embeddings, in such a way that the result is again a plane graph. All essentially different embeddings are generated.