A123542 Triangular array T(n,k) giving number of 3-connected graphs with n labeled nodes and k edges (n >= 4, ceiling(3*n/2) <= k <= n(n-1)/2).

1, 15, 10, 1, 70, 492, 690, 395, 105, 15, 1, 5040, 28595, 58905, 63990, 42392, 18732, 5880, 1330, 210, 21, 1, 16800, 442680, 2485920, 6629056, 10684723, 11716068, 9409806, 5824980, 2872317, 1147576, 373156, 98112, 20475, 3276

Offset: 4

Author

N. J. A. Sloane, Nov 13 2006

Keywords

• nonn
• tabf

Examples

			Triangle begins:
n = 4
k = 6 : 1
Total( 4) = 1
n = 5
k = 8 : 15
k = 9 : 10
k = 10 : 1
Total( 5) = 26
n = 6
k = 9 : 70
k = 10 : 492
k = 11 : 690
k = 12 : 395
k = 13 : 105
k = 14 : 15
k = 15 : 1
Total( 6) = 1768
n = 7
k = 11 : 5040
k = 12 : 28595
k = 13 : 58905
k = 14 : 63990
k = 15 : 42392
k = 16 : 18732
k = 17 : 5880
k = 18 : 1330
k = 19 : 210
k = 20 : 21
k = 21 : 1
Total( 7) = 225096
		

References

• R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.

Links

• R. W. Robinson, Rows 4 through 15, flattened (row 15 is incomplete).
• T. R. S. Walsh, Counting labeled three-connected and homeomorphically irreducible two-connected graphs, J. Combin. Theory Ser. B 32 (1982), no. 1, 1-11, Table 1.

Crossrefs

Row sums give A005644. Cf. A123527, A123534.