Hasheminezhad, MahdiehMcKay, BrendanReeves, Tristan2015-12-101526-1719http://hdl.handle.net/1885/59153We 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 construc- tion 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 pen- tangulations with minimum degree 2.Author/s retain copyright201110.7155/jgaa.002322015-12-10