Enumerating planar locally finite Cayley graphs

Details Enumerating planar locally finite Cayley graphs Enumerating planar locally finite Cayley graphs

2003-09-11

arxiv.org/abs/cs/0309017v1

Computer Science

Discrete Mathematics

19 pages, 6 PostScript figures, 12 embedded PsTricks figures. An additional file (~ 438ko.) containing the figures in appendix

Scientific paper

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

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