Counting edge-transitive, one-ended, three-connected planar maps with a given growth rate.

Abstract

B. Grünbaum and G. C. Shephard have classified one-ended, 3-connected, planar, edge-transitive maps. It turns out that each of these maps can be described uniquely by an edge-symbol ‹p, q; k, ℓ›. Recently the growth rate of each of these maps has been determined by S. Graves, T. Pisanski and M. E. Watkins. We determine the number of edge-transitive maps for a given growth rate.