OFFSET
1,5
COMMENTS
T(n,1) = T(n,n) = 1 (here we count the empty graph and the complete graph). T(n,n-1) = n-1 (here we count the graphs with clique number equal to n-1). - Geoffrey Critzer, Oct 12 2016
Row sums give A000088. - Joerg Arndt, Oct 13 2016
LINKS
Keith Briggs, combinatorial graph theory, see entry "number of graphs on n nodes with clique number k".
FindStat - Combinatorial Statistic Finder, The chromatic number of a graph.
Eric Weisstein's World of Mathematics, Chromatic Number
Eric Weisstein's World of Mathematics, n-Chromatic Graph
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 6, 3, 1;
1, 12, 16, 4, 1;
1, 34, 84, 31, 5, 1;
1, 87, 579, 318, 52, 6, 1;
1, 302, 5721, 5366, 867, 81, 7, 1;
1, 1118, 87381, 155291, 28722, 2028, 118, 8, 1;
1, 5478, 2104349, 7855628, 1919895, 115391, 4251, 165, 9, 1;
...
PROG
(Sage) # prints triangle with a leading zero in each row
for n in range(1, 8) :
st = [0 for j in range(n+1)]
G = graphs(n)
for g in G :
st[ g.chromatic_number() ] += 1
print(st)
# Joerg Arndt, Oct 13 2016
CROSSREFS
Row sums are A000088.
KEYWORD
nonn,tabl
AUTHOR
Eric W. Weisstein, May 24 2003
EXTENSIONS
Offset corrected by Joerg Arndt, Oct 13 2016
a(36)-a(55) from Joerg Arndt, Oct 15 2016
a(56)-a(66) from Andrew Howroyd, Dec 02 2018
STATUS
approved