Graph Isomorphism Algorithm by Perfect Matching

  • Kazuma Fukuda
  • Mario Nakamori
Conference paper
Part of the IFIP — The International Federation for Information Processing book series (IFIPAICT, volume 130)

Abstract

No polynomial time algorithm is known for the graph isomorphism problem. In this paper, we determine graph isomorphism with the help of perfect matching algorithm, to limit the range of search of 1 to 1 correspondences between the two graphs: We reconfigure the graphs into layered graphs, labeling vertices by partitioning the set of vertices by degrees. We prepare a correspondence table by means of whether labels on 2 layered graphs match or not. Using that table, we seek a 1 to 1 correspondence between the two graphs. By limiting the search for 1 to 1 correspondences between the two graphs to information in the table, we are able to determine graph isomorphism more efficiently than by other known algorithms. The algorithm was timed with on experimental data and we obtained a complextity of O(n 4).

Keywords

Graph Isomorphism Regular Graph 
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Copyright information

© IFIP International Federation for Information Processing 2003

Authors and Affiliations

  • Kazuma Fukuda
    • 1
  • Mario Nakamori
    • 2
  1. 1.Department of Internet Media Sysytem, Information Technology R&D CenterMITSUBISHI ELECTRIC CorporationKamakura, KanagawaJapan
  2. 2.Department of Computer ScienceTokyo A&T UniversityKoganei, TokyoJapan

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