A planar connected graph is a graph which is both planar and connected. The numbers of planar connected graphs with n = 1, 2, ... nodes are 1, 1, 2, 6, 20, 99, 646, 5974, 71885, ... (OEIS A003094; Steinbach 1990, p. 131). A subset of planar 3-connected graphs are called polyhedral graphs. The following table gives the numbers of planar connected graphs having minimal degrees of at least k. k | OEIS | n = 1, 2, 3, ... 2 | A054381 | 0, 0, 1, 3, 10, 49, 332, ... The numbers of planar connected graphs with n = 1, 2, ... edges are 1, 1, 3, 5, 12, 30, 79, 227, 709, 2318, ... (OEIS A046091).

connected graph | planar graph | polyhedral graph | polynema