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# Recursive generation of simple planar 5-regular graphs and pentangulations

@article{Hasheminezhad2011RecursiveGO, title={Recursive generation of simple planar 5-regular graphs and pentangulations}, author={Mahdieh Hasheminezhad and Brendan D. McKay and Tristan Reeves}, journal={J. Graph Algorithms Appl.}, year={2011}, volume={15}, pages={417-436} }

- Published 2011 in J. Graph Algorithms Appl.

We describe how the 5-regular simple planar graphs can all be obtained from an elementary family of starting graphs by repeatedly applying a few local expansion operations. The proof uses an amalgam of theory and computation. By incorporating the recursion into the canonical construction path method of isomorph rejection, a generator of non-isomorphic embedded 5-regular planar graphs is obtained with time complexity O(n) per isomorphism class. A similar result is obtained for simple planar… CONTINUE READING