| Abstract: | Orderly algorithms for the generation of exhaustive lists of nonisomorphic graphs are discussed. The existence of orderly methods to generate the graphs with a given subgraph and without a given subgraph is established. This method can be used to list all the nonisomorphic subgraphs of a given graph, as well as to produce catalogs of Hamiltonian graphs, pancyclic graphs, degree-constrained graphs, and other classes. A generalization of this method is given that can be used to generate lists of graphs with given girth, planar graphs, k-colorable graphs, and k-connected graphs, for example. Finally, these observations are employed to generate restricted classes of digraphs, notably acyclic digraphs and poset digraphs. The generation of poset digraphs is shown to supply a practical orderly method for producing a catalog of lattices. Similar observations concerning vertex addition generation methods allow one to improve on existing methods for the generation of catalog of interval and circle graphs. |
