Recursive Generation of 5-Regular Planar Graphs

Authors:
Mahdieh Hasheminezhad;Brendan D. Mckay;Tristan Reeves
Affiliations:
Department of Computer Science Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran;Department of Computer Science, Australian National University, Australia ACT 0200;Polytopia Systems Pty. Ltd., Mawson, Australia 2607
Venue:
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Year:
2009

Citing 3
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Abstract

We describe for the first time 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 innovative 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 2) per isomorphism class.