Edge‐transitive planar graphs
Branko Grünbaum, Geoffrey C. Shephard · Journal of Graph Theory · 1987
Abstract Graphs which are more or less “symmetric” in one sense or another have been the subject of many investigations. In particular, finite graphs in which all edges are equivalent under isomorphisms of the graph have attracted some attention (see, for example, Fleischner and Imrich [2], Grünbaum and Shephard [5]). Here we extend this investigation to infinite planar graphs which are “reasonable” in the sense that they have locally‐finite plane embeddings. The purpose of this paper is to give a complete enumeration of such graphs, both finite and infinite. We remark that the seemingly similar problem of determining all planar graphs in which the vertices are equivalent under isomorphisms of the graph appears to be much harder, and at present we are very far from a solution.