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A187928 Number of embeddings on the sphere of 2-connected planar graphs, minimum vertex degree 3, with n edges. 1
1, 1, 4, 15, 42, 135, 440, 1480, 5106, 17890, 63264, 226018, 812354, 2936837, 10666188, 38901190, 142386358 (list; graph; refs; listen; history; text; internal format)
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 A240359 A282522

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

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Last modified May 23 14:53 EDT 2017. Contains 286925 sequences.