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Great Lakes CS Conference on New Research Results in Computer Science

Great Lakes CS 1989: Computing in the 90's pp 1–7Cite as

Computational complexity of geometric symmetry detection in graphs

  • Track1: Graph Algorithms
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 507))

Abstract

Constructing a visually informative drawing of an abstract graph is a problem of considerable practical importance, and has recently been the focus of much investigation. Displaying symmetry has emerged as one of the foremost criteria for achieving good drawings. Linear-time algorithms are already known for the detection and display of symmetry in trees, outerplanar graphs, and embedded planar graphs. The central results of this paper show that for general graphs, however, detecting the presence of even a single axial or rotational symmetry is NP-complete. A number of related results are also established, including the #P-completeness of counting the axial or rotational symmetries of a graph.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Missouri - Rolla, 65401, Rolla, MO, USA

    Joseph Manning

Authors
  1. Joseph Manning
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Editor information

Naveed A. Sherwani Elise de Doncker John A. Kapenga

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© 1991 Springer-Verlag Berlin Heidelberg

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Manning, J. (1991). Computational complexity of geometric symmetry detection in graphs. In: Sherwani, N.A., de Doncker, E., Kapenga, J.A. (eds) Computing in the 90's. Great Lakes CS 1989. Lecture Notes in Computer Science, vol 507. Springer, New York, NY. https://doi.org/10.1007/BFb0038465

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  • DOI: https://doi.org/10.1007/BFb0038465

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97628-0

  • Online ISBN: 978-0-387-34815-5

  • eBook Packages: Springer Book Archive

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