Geodesic
Recursive generation of simple planar 5-regular graphs and pentangulations
Journal of Graph Algorithms and Applications, Special Issue on Selected Papers from the Third Annual Workshop on Algorithms and Computation (WALCOM 2009) , Tome 15 (2011) no. 3, pp. 417-436.

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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(n2) per isomorphism class. A similar result is obtained for simple planar pentangulations with minimum degree 2.
DOI : 10.7155/jgaa.00232
Keywords: planar graph, regular, pentangulation, algorithm 
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Mahdieh Hasheminezhad; Brendan McKay; Tristan Reeves. Recursive generation of simple planar 5-regular graphs and pentangulations. Journal of Graph Algorithms and Applications, 
							Special Issue on Selected Papers from the Third Annual Workshop on Algorithms and Computation (WALCOM 2009)
					, Tome 15 (2011) no. 3, pp. 417-436. doi : 10.7155/jgaa.00232. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00232/

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