Enumerating planar locally finite Cayley graphs [article]

David Renault
2003 arXiv   pre-print
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
arXiv:cs/0309017v1 fatcat:m4pdgbgujndq5gytl3cjfbnewa