2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229561Planar 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.12 pagesGroup Theory20F32, 05C25text