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Computing Automorphism Groups of Chordal Graphs Whose Simplicial Components Are of Small Size
IEICE TRANSACTIONS on Information and Systems
Publication Date: 2006/08/01
Online ISSN: 1745-1361
Print ISSN: 0916-8532
Type of Manuscript: INVITED PAPER (Special Section on Invited Papers from New Horizons in Computing)
chordal graph, simplicial component, automorphism, isomorphism, computational group theory, algorithm, computational complexity,
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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.