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}
}
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

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