Geometric automorphism groups of graphs

Authors:
David Abelson;Seok-Hee Hong;D. E. Taylor
Affiliations:
School of Mathematics and Statistics, University of Sydney, Australia;NICTA and School of Information Technologies, University of Sydney, Australia;School of Mathematics and Statistics, University of Sydney, Australia
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

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 an n-geometric automorphism group as a subgroup of the 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 given graph. We implement the algorithm using Magma [] and the experimental results show that our approach is very efficient in practice. We also present a drawing algorithm to display 2- and 3-geometric automorphism groups.