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The vertex-transitive TLF-planar graphs

D. Renault
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Abstract

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.

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D. Renault. 2004-12-17. The vertex-transitive TLF-planar graphs. https://arxiv.org/abs/cs/0412078

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