A187928 Number of embeddings on the sphere of planar graphs with n edges having connectivity exactly 2 and minimum vertex degree at least 3.

1, 2, 4, 15, 42, 135, 440, 1480, 5106, 17890, 63264, 226018, 812354, 2936837, 10666188, 38901190, 142386358

Offset: 10

Author

Stuart E Anderson, Mar 16 2011

Keywords

• nonn
• more
• hard

Comments

The graphs are 2-connected, but not 3-connected. The graphs were enumerated using plantri (by B.D. McKay & G. Brinkmann) for the purpose of finding compound perfect squared squares. If all graphs with n edges are generated then all compound squares in order n-1 can be obtained from them. Graphs with minimum degree at least 3 are also called homeomorphically irreducible.

Links

• Stuart Anderson, Compound Perfect Squared Squares
• B. D. McKay and G. Brinkmann, Plantri Guide
• Gunnar Brinkmann and Brendan McKay, Guide to using plantri [Cached copy, with permission]

Crossrefs

Antidiagonal sums of A378077.

Cf. A034889, A181340, A187927, A021103, A378076.

Programs

plantri

plantri -p -c2 -m3 -e# -x -u -v n

plantri

plantri -pc2m3e#xuv n # to count graphs by node number (n) and edge number (#)

Extensions

a(22) corrected by Stuart E Anderson, Feb 24 2013

a(23)-a(26) from Lorenz Milla, Oct 08 2013

a(11) corrected by Andrew Howroyd, Nov 15 2024