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

Seinosuke TODA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E89-D   No.8   pp.2388-2401
Publication Date: 2006/08/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e89-d.8.2388
Print ISSN: 0916-8532
Type of Manuscript: INVITED PAPER (Special Section on Invited Papers from New Horizons in Computing)
Category: 
Keyword: 
chordal graph,  simplicial component,  automorphism,  isomorphism,  computational group theory,  algorithm,  computational complexity,  

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Summary: 
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.