Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an