A187928 Number of embeddings on the sphere of 2-connected planar graphs, minimum vertex degree 3, with n edges.

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

Offset

10,3

Comments

The graphs are exactly 2-connected, not at least 2-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 3 are also called homeomorphically irreducible.

Links

Table of n, a(n) for n=10..26.

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]

Prog

use;
plantri -p -c2 -m3 -e# -x -u -v n  ; or
plantri -pc2m3e#xuv n
to count graphs by node number (n) and edge number (#)

Crossrefs

Cf. A034889, A181340, A187927, A021103.

Sequence in context: A100503 A085829 A085567 * A213498 A294259 A240359

Adjacent sequences: A187925 A187926 A187927 * A187929 A187930 A187931

Keyword

nonn,more,hard

Author

Stuart E Anderson, Mar 16 2011

Extensions

Corrected a(22) - Stuart E Anderson, Feb 24 2013

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

Status

approved