Enumerating planar locally finite Cayley graphs

2003/09/11 by David Renault, Renault, David
Computer Science · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #G.2.2 #cs.DM

paper · pdf · doi:10.48550/arxiv.cs/0309017

19 pages, 6 PostScript figures, 12 embedded PsTricks figures. An additional file (~ 438ko.) containing the figures in appendix might be found at http://www.labri.fr/Perso/~renault/research/pages.ps.gz

arxiv created 2003/09/11 · arxiv updated 2009/12/01

Abstract

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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