Enumerating planar locally finite Cayley graphs

@article{Renault2003EnumeratingPL,
  title={Enumerating planar locally finite Cayley graphs},
  author={David Renault},
  journal={CoRR},
  year={2003},
  volume={cs.DM/0309017}
}
We characterize the set of planar locally finite Cayley graphs, and give a finite representation of these graphs by a special kind of finite state automata called labeling schemes. As a result, we are able to enumerate and describe all planar locally finite Cayley graphs of a given degree. This analysis allows us to solve the problem of decision of the locally finite planarity for a word-problem-decidable presentation. 

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