Automatic Enumeration of Acyclic Graphs with Simple and Hyper Edges

This paper presents a systematic and computerized mathematical representation to represent the topological structure of acyclic graphs with simple and hyper edges. Based on the mathematical representation, a multiplication process is presented to synthesize acyclic graphs with p vertices from those with p  1 vertices. The Topological Code of graphs is applied to identify the isomorphism of acyclic graphs efficiently. Then, an algorithm is developed for the automatic enumeration of acyclic graphs with simple and hyper edges. Finally, catalogs of acyclic graphs up to seven vertices are listed.