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Finding Planar Geometric Automorphisms in Planar Graphs

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Algorithms and Computation (ISAAC 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1533))

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Abstract

Drawing a graph symmetrically enables an understanding of the entire graph to be built up from that of smaller subgraphs. This paper discusses symmetric drawings of planar graphs. More specifically, we discuss planar geometric automorphisms, that is, automorphisms of a graph G that can be represented as symmetries of a planar drawing of G. Finding planar geometric automorphisms is the first and most difficult step in constructing planar symmetric drawings of graphs. The problem of determining whether a given graph has a nontrivial geometric automorphism is NP-complete for general graphs. In this paper, we present a polynomial time algorithm for finding planar geometric automorphisms of graphs.

This research has been supported by KOSEF No.971-0907-045-1, the Australian Research Council, and the SCARE project at the University of Limerick. This paper was partially written when the first author was visiting the University of Newcastle, and partially written while the first two authors were visiting the University of Limerick.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering Ewha, Womans University, Korea

    Seok-Hee Hong & Sang-Ho Lee

  2. Department of Computer Science and Software Engineering, University of Newcastle, Australia

    Peter Eades

Authors
  1. Seok-Hee Hong
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  2. Peter Eades
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  3. Sang-Ho Lee
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Korea Advanced Institute of Science and Technology, 373-1, Kusong-dong, Yusong-gu, Taejon, 305-701, Korea

    Kyung-Yong Chwa

  2. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

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© 1998 Springer-Verlag Berlin Heidelberg

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Hong, SH., Eades, P., Lee, SH. (1998). Finding Planar Geometric Automorphisms in Planar Graphs. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_30

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  • DOI: https://doi.org/10.1007/3-540-49381-6_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65385-1

  • Online ISBN: 978-3-540-49381-5

  • eBook Packages: Springer Book Archive

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