Geometric symmetry in graphs
Fast detection and display of symmetry in outerplanar graphs
Discrete Applied Mathematics
Spring Algorithms and Symmetry
COCOON '97 Proceedings of the Third Annual International Conference on Computing and Combinatorics
Drawing Algorithms for Series-Parallel Digraphs in Two and Three Dimensions
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Isomorphism problems involving planar graphs.
Isomorphism problems involving planar graphs.
Graph Theory With Applications
Graph Theory With Applications
A V log V algorithm for isomorphism of triconnected planar graphs
Journal of Computer and System Sciences
An Algorithm for Finding Three Dimensional Symmetry in Series Parallel Digraphs
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
On Maximum Symmetric Subgraphs
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
An Algorithm for Finding Three Dimensional Symmetry in Trees
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
A Group-Theoretic Method for Drawing Graphs Symmetrically
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
A linear time algorithm for constructing maximally symmetric straight-line drawings of planar graphs
GD'04 Proceedings of the 12th international conference on Graph Drawing
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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.