The vertex-transitive TLF-planar graphs
<|reference_start|>The vertex-transitive TLF-planar graphs: We consider the class of the topologically locally finite (in short TLF) planar vertex-transitive graphs, a class containing in particular all the one-ended planar Cayley graphs and the normal transitive tilings. We characterize these graphs with a finite local representation and a special kind of finite state automaton named labeling scheme. As a result, we are able to enumerate and describe all TLF-planar vertex-transitive graphs of any given degree. Also, we are able decide to whether any TLF-planar transitive graph is Cayley or not.<|reference_end|>
@article{renault2004the,
    title={The vertex-transitive TLF-planar graphs},
    author={D. Renault},
    journal={arXiv preprint arXiv:cs/0412078},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0412078},
    primaryClass={cs.DM}
}