A122083 Triangle read by rows in which row n gives the number of unlabeled bicolored graphs having k nodes of one color and n-k nodes of the other color, with no isolated nodes; the color classes are not interchangeable.
1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 3, 1, 0, 0, 1, 5, 5, 1, 0, 0, 1, 8, 17, 8, 1, 0, 0, 1, 11, 42, 42, 11, 1, 0, 0, 1, 15, 91, 179, 91, 15, 1, 0, 0, 1, 19, 180, 633, 633, 180, 19, 1, 0, 0, 1, 24, 328, 2001, 3835, 2001, 328, 24, 1, 0, 0, 1, 29, 565, 5745, 20755, 20755
Offset: 0
Examples
K M N Gives the number N of unlabeled bicolored graphs with no isolated nodes and having K nodes of one color and M nodes of the other color. 0 0 1 Total( 0)= 1 0 1 0 1 0 0 Total( 1)= 0 0 2 0 1 1 1 2 0 0 Total( 2)= 1 0 3 0 1 2 1 2 1 1 3 0 0 Total( 3)= 2 0 4 0 1 3 1 2 2 3 3 1 1 4 0 0 Total( 4)= 5 0 5 0 1 4 1 2 3 5 3 2 5 4 1 1 5 0 0 Total( 5)= 12 0 6 0 1 5 1 2 4 8 3 3 17 4 2 8 5 1 1 6 0 0 Total( 6)= 35
References
- J. G. Lee, Almost Distributive Lattice Varieties, Algebra Universalis, 21 (1985), 280-304.
- R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
Links
- R. W. Robinson, First 20 rows, flattened
- F. Harary, L. March and R. W. Robinson, On enumerating certain design problems in terms of bicolored graphs with no isolates, Environment and Planning, B 5 (1978), 31-43. See Table 2.
- F. Harary, L. March and R. W. Robinson, On enumerating certain design problems in terms of bicolored graphs with no isolates, Environment and Planning B: Urban Analytics and City Science, 5 (1978), 31-43. [Annotated scanned copy] See Table 2.