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

Authors:
Seinosuke Toda
Affiliations:
The author is with the Department of Computer Science and System Analysis, College of Humanities and Sciences, Nihon University, Tokyo, 156--8550 Japan. E-mail: toda@cssa.chs.nihon-u.ac.jp
Venue:
IEICE - Transactions on Information and Systems
Year:
2006

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Abstract

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.