Journal of Graph Algorithms and Applications
http://jgaa.info ISSN: 1526-1719
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DOI: 10.7155/jgaa.00272 Generating Geometric Graphs Using Automorphisms Gregory McColm 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.
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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 |
| Journal of Graph Algorithms and Applications |