English

The vertex-transitive TLF-planar graphs

Discrete Mathematics 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.cs/0412078,
  title  = {The vertex-transitive TLF-planar graphs},
  author = {D. Renault},
  journal= {arXiv preprint arXiv:cs/0412078},
  year   = {2007}
}

Comments

Article : 23 pages, 15 figures Appendix : 13 pages, 72 figures Submitted to Discrete Mathematics The appendix is accessible at http://www.labri.fr/~renault/research/research.html