Journal of Graph Algorithms and Applications
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Generating Geometric Graphs Using Automorphisms
Vol. 16, no. 2, pp. 507-541, 2012. Regular paper.
Abstract 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.
Submitted: October 2010.
Reviewed: January 2012.
Revised: March 2012.
Reviewed: May 2012.
Revised: July 2012.
Accepted: July 2012.
Final: August 2012.
Published: August 2012.
Communicated by Giuseppe Liotta