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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, 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
1,5
COMMENTS
The concept of the packing chromatic number was introduced by Goddard et al. (2008) under the name broadcast chromatic number. The term packing chromatic number was introduced by Brešar et al. (2007).
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) = 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.)
EXAMPLE
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
CROSSREFS
Cf. A000041, A000088 (row sums), A084268 (chromatic number), A275622 (cubic graphs), A335203 (hypercube graph) A362580 (square grid graph), A363044 (connected).
Sequence in context: A057785 A305882 A339285 * A192404 A373746 A291261
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved