A391133 The number of connected planar graphs on n unlabeled vertices with connected planar complement.

1, 0, 0, 1, 8, 68, 454, 1962

Offset

1,5

Comments

This sequence is finite and there are no additional terms.

Links

Table of n, a(n) for n=1..8.

Prog

(SageMath)
def a(n):
    count = 0
    for G in graphs(n):
        C = G.complement()
        if G.is_planar() and G.is_connected() and C.is_planar() and C.is_connected():
            count += 1
    return count
for n in range(1, 10): print(a(n))

Crossrefs

Cf. A391132 (not necessarily connected).

Sequence in context: A050841 A208947 A296670 * A263477 A249390 A190510

Adjacent sequences: A391130 A391131 A391132 * A391134 A391135 A391136

Keyword

nonn,fini,full

Author

Jim Nastos, Nov 30 2025

Status

approved