Enumerating planar locally finite Cayley graphs
<|reference_start|>Enumerating planar locally finite Cayley graphs: 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.   Keywords: vertex-transitive, Cayley graph, planar graph, tiling, labeling scheme<|reference_end|>
@article{renault2003enumerating,
    title={Enumerating planar locally finite Cayley graphs},
    author={David Renault},
    journal={arXiv preprint arXiv:cs/0309017},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0309017},
    primaryClass={cs.DM}
}