Enumerating planar locally finite Cayley graphs
离散数学
2007-05-23 v1
摘要
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
引用
@article{arxiv.cs/0309017,
title = {Enumerating planar locally finite Cayley graphs},
author = {David Renault},
journal= {arXiv preprint arXiv:cs/0309017},
year = {2007}
}
备注
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