Skip to main content
SpringerLink
Log in

Computing Graph Automorphism from Partial Solutions

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript

Abstract

It is known that, given two isomorphic graphs G and H, finding a pair of vertices (v i ,w j ) where v i is mapped to w j by an isomorphism from G to H is as hard as computing an isomorphism from G to H. In this paper, we prove a similar result for the Graph Automorphism problem. That is to say, we prove that, given a graph that has a non-trivial automorphism, finding a pair of vertices (v i ,v j ) where v i is mapped to v j by a non-trivial automorphism on the graph is as hard as computing a non-trivial automorphism on the graph.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gál, A., Halevi, S., Lipton, R., Petrank, E.: Computing from partial solutions. In: Proceedings of the 14th Annual IEEE Conference on Computational Complexity, pp. 34–45. IEEE Computer Society Press, Los Alamitos (1999)

    Google Scholar 

  2. Große, A., Rothe, J., Wechsung, G.: Relating partial and complete solutions and the complexity of computing smallest solutions. In: Proceedings of the Seventh Italian Conference on Theoretical Computer Science. Lecture Notes in Computer Science, vol. 2202, pp. 339–356. Springer, Berlin (2001)

    Google Scholar 

  3. Große, A., Rothe, J., Wechsung, G.: Computing complete graph isomorphisms and Hamiltonian cycles from partial ones. Theory Comput. Syst. 35, 81–93 (2002)

    MATH  MathSciNet  Google Scholar 

  4. Köbler, J., Schöning, U., Torán, J.: The Graph Isomorphism Problem: Its Structural Complexity. Birkhäuser, Basel (1993)

    MATH  Google Scholar 

  5. Lozano, A., Torán, J.: On the nonuniform complexity of the graph isomorphism problem. In: Proceedings of the 7th Structure in Complexity Theory Conference, pp. 118–129, 1992

  6. Lubiw, A.: Some NP-complete problems similar to graph isomorphism. SIAM J. Comput. 10, 11–21 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  7. Read, R.C., Corneil, D.G.: The graph isomorphism disease. J. Graph Theory 1, 339–363 (1977)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Tokyo Denki University, Hatoyama, Saitama, 350-0394, Japan

    Takayuki Nagoya

Authors
  1. Takayuki Nagoya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Takayuki Nagoya.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nagoya, T. Computing Graph Automorphism from Partial Solutions. Theory Comput Syst 44, 356–368 (2009). https://doi.org/10.1007/s00224-007-9077-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00224-007-9077-7

Keywords

Search

Navigation