A363043 Triangle read by rows: T(n,k) is the number of unlabeled graphs with n nodes and packing chromatic number k, 1 <= k <= n.
1, 1, 1, 1, 2, 1, 1, 4, 5, 1, 1, 6, 15, 11, 1, 1, 10, 42, 73, 29, 1, 1, 14, 109, 390, 439, 90, 1, 1, 21, 278, 1953, 5546, 4188, 358, 1, 1, 29, 687, 9085, 61023, 134183, 67888, 1771, 1, 1, 41, 1694, 40344, 572235, 3517101, 5860434, 2001582, 11735, 1
Offset: 1
Examples
Triangle begins: n\k| 1 2 3 4 5 6 7 8 9 10 ---+-------------------------------------------------------- 1 | 1 2 | 1 1 3 | 1 2 1 4 | 1 4 5 1 5 | 1 6 15 11 1 6 | 1 10 42 73 29 1 7 | 1 14 109 390 439 90 1 8 | 1 21 278 1953 5546 4188 358 1 9 | 1 29 687 9085 61023 134183 67888 1771 1 10 | 1 41 1694 40344 572235 3517101 5860434 2001582 11735 1
Links
- Boštjan Brešar, Sandi Klavžar, and Douglas F. Rall, On the packing chromatic number of Cartesian products, hexagonal lattice, and trees, Discrete Applied Mathematics 155 (2007), 2303-2311.
- Wayne Goddard, Sandra M. Hedetniemi, Stephen T. Hedetniemi, John M. Harris, and Douglas F. Rall, Broadcast chromatic numbers of graphs, Ars Combinatoria 86 (2008), 33-49.
Crossrefs
Formula
T(n,1) = 1. (The only graphs with packing chromatic number 1 are the graphs with no edges.)
T(n,2) = A000041(n)-1. (The only graphs with packing chromatic number 2 are those consisting of star graph components, with at least one of the components containing more than one node.)
T(n,n) = 1. (The only graph with n nodes and packing chromatic number n is the complete graph on n nodes.)
Comments