A393183 Number of non-isomorphic planar graphs with n edges that are exactly 2-vertex connected and at least 3-edge connected.

1, 2, 3, 12, 31, 93, 277, 871, 2794, 9218, 30890, 105229, 362643, 1263008, 4436651

Offset

10,2

Comments

This sequence counts graphs H with n edges that satisfy vertex connectivity K(H) = 2 and edge connectivity l(H) >= 3.

These graphs arise naturally as the diagonal graphs (also known as face graphs) in the dual decomposition of 4-regular planar graphs. Specifically, they constitute the set of unique structural components used to construct the subclass of polyhedra counted in A392848.

Links

Table of n, a(n) for n=10..24.

Gunnar Brinkmann, Heidi Van den Camp and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.

Samuel Kamperis, Enumeration of planar graphs are exactly 2-vertex connected and at least 3-edge connected, including updates for a(23) and a(24).

Crossrefs

Cf. A392848.

Sequence in context: A034381 A076424 A165301 * A072440 A135522 A353831

Adjacent sequences: A393180 A393181 A393182 * A393184 A393185 A393186

Keyword

nonn,more

Author

Samuel Kamperis, Feb 04 2026

Extensions

a(23)-a(24) from Samuel Kamperis, May 04 2026

Status

approved