Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs

Authors:
Ryuhei Uehara;Seinosuke Toda;Takayuki Nagoya
Affiliations:
Natural Science Faculty, Komazawa University, 1-23-1 Komazawa, Setagaya-Ku, Tokyo 154-8525, Japan and University of Waterloo;Department of Computer Science and System Analysis, College of Humanities and Sciences, Nihon University, 3-25-40 Sakurajosui, Setagaya-Ku, Tokyo 156-8550, Japan;Department of Mathematical Science, College of Sceince and Engineering, Tokyo Denki University, Hatoyama, Saitama 350-0394, Japan
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

This paper deals with the graph isomorphism (GI) problem for two graph classes: chordal bipartite graphs and strongly chordal graphs. It is known that GI problem is GI complete even for some special graph classes including regular graphs, bipartite graphs, chordal graphs, comparability graphs, split graphs, and k-trees with unbounded k. On the other hand, the relative complexity of the GI problem for the above classes was unknown. We prove that deciding isomorphism of the classes are GI complete.