A Group-Theoretic Method for Drawing Graphs Symmetrically
Abelson, David and Hong, Seok-Hee and Donald E., Taylor (2002) A Group-Theoretic Method for Drawing Graphs Symmetrically. In: Graph Drawing 10th International Symposium, GD 2002, August 26-28, 2002, Irvine, CA, USA , pp. 86-97 (Official URL: http://dx.doi.org/10.1007/3-540-36151-0_9).
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Constructing symmetric drawings of graphs is NP-hard. In this paper, we present a new method for drawing graphs symmetrically based on group theory. More formally, we define a n-geometric automorphism group of a graph that can be displayed as symmetries of a drawing of the graph in n dimensions. Then we present an algorithm to find all 2- and 3-geometric automorphism groups of a graph. We implement the algorithm using Magma  and the experimental results shows that our approach is very efficient in practice. We also present a drawing algorithm to display a 2- or 3-geometric automorphism group.
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