Computing Automorphism Groups of Chordal Graphs Whose Simplicial Components Are of Small Size

It is known that any chordal graph can be uniquely decomposed into simplicial components. Based on this fact, it is shown that for a given chordal graph, its automorphism group can be computed in O((c! · n)O(1)) time, where c denotes the maximum size of simplicial components and n denotes the number of nodes. It is also shown that isomorphism of those chordal graphs can be decided within the same time bound. From the viewpoint of polynomial-time computability, our result strictly strengthens the previous ones respecting the clique number.