David Abelson, SeokHee Hong and Don E. Taylor, Geometric Automorphism Groups of Graphs, Discrete Applied Mathematics, 155(17), pp. 22112226, 2007, Elsevier.
Constructing symmetric drawings of graphs is NPhard. In
this paper, we present a new method for drawing graphs symmetrically
based on group theory. More formally, we define an ngeometric 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 3geometric
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 3geometric automorphism groups.
