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arXiv · 0708.0920

Planar graphs and covers

M. J. Dunwoody
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Abstract

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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M. J. Dunwoody. 2009-05-08. Planar graphs and covers. https://arxiv.org/abs/0708.0920

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