A363044 Triangle read by rows: T(n,k) is the number of unlabeled connected graphs with n nodes and packing chromatic number k, 1 <= k <= n.
1, 0, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 9, 10, 1, 0, 1, 21, 61, 28, 1, 0, 1, 48, 305, 409, 89, 1, 0, 1, 109, 1475, 5077, 4097, 357, 1, 0, 1, 247, 6623, 55005, 129904, 67529, 1770, 1, 0, 1, 564, 28540, 505098, 3378636, 5792187, 1999810, 11734, 1
Offset: 1
Examples
Triangle begins: n\k| 1 2 3 4 5 6 7 8 9 10 ---+------------------------------------------------------- 1 | 1 2 | 0 1 3 | 0 1 1 4 | 0 1 4 1 5 | 0 1 9 10 1 6 | 0 1 21 61 28 1 7 | 0 1 48 305 409 89 1 8 | 0 1 109 1475 5077 4097 357 1 9 | 0 1 247 6623 55005 129904 67529 1770 1 10 | 0 1 564 28540 505098 3378636 5792187 1999810 11734 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.
Formula
T(n,1) = 0 for n >= 2. (The only connected graph with packing chromatic number 1 is the 1-node graph.)
T(n,2) = 1 for n >= 2. (The only connected graphs with packing chromatic number 2 are the star graphs on at least 2 nodes.)
T(n,n) = 1. (The only connected graph with n nodes and packing chromatic number n is the complete graph on n nodes.)
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