English

Planar graphs and covers

Group Theory 2009-05-08 v2

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.

Keywords

Cite

@article{arxiv.0708.0920,
  title  = {Planar graphs and covers},
  author = {M. J. Dunwoody},
  journal= {arXiv preprint arXiv:0708.0920},
  year   = {2009}
}

Comments

12 pages

R2 v1 2026-06-21T09:05:27.243Z