Planar graphs and covers

Details Planar graphs and covers Planar graphs and covers

2007-08-07

arxiv.org/abs/0708.0920v2

Mathematics

Group Theory

12 pages

Scientific paper

Planar locally finite graphs which are almost vertex transitive are discussed. If the graph is 3-connected and has at most one end then the group of automorphisms is a planar discontinuous group and its structure is well-known. A general result is obtained for such graphs where no restriction is put on the number of ends. It is shown that such a graph can be built up from one ended or finite planar graphs in a precise way. The results give a classification of the finitely generated groups with planar Cayley graphs.

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