Computational complexity of geometric symmetry detection in graphs

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


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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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Joseph Manning
    • 1
  1. 1.Department of Computer ScienceUniversity of Missouri - RollaRollaUSA

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