Efficient Non-isomorphic Graph Enumeration Algorithms for Subclasses of Perfect Graphs

Intersection graphs are well-studied in the area of graph algorithms. Some intersection classes known to have algorithms enumerating all unlabeled by reverse search. Since these output one and numbers vast, they work only for a small number vertices. Binary decision diagrams (BDDs) compact data structures various types useful solving optimization enumeration problems. This study proposes five classes, which admit $$\textrm{O}(n)$$ -bit string representations their member graphs. Our algorithm each class enumerates with n vertices over BDDs representing binary strings time polynomial n. Moreover, our extended enumerate those constraints on maximum (bi)clique size and/or edges.