Generating Geometric Graphs Using Automorphisms - McColm, Gregory (Journal of Graph Algorithms and Applications, 2012)
We outline an algorithm for generating nets, a "net" being a geometric graph embedded in a space on which some group acts transitively.We prove that any connected net in such a space can be generated by this process, which can also be regarded as a covering of the net by copies of a connected "transversal" subnet.This paper outlines some of the underlying theory supporting a crystal prediction and design program currently under development.The paper begins with some background in geometric group theory.