A 
-chromatic
graph is a graph 
having chromatic number 
(Harary 1994, p. 127).
In contrast, a graph having 
is said to be a k-colorable
graph. A graph is one-colorable iff
it is totally disconnected (i.e., is an empty graph).
There are 1, 2, 6, and 12 distinct 2-chromatic simple graphs on 
,
..., 5 nodes. Examples are illustrated above.
The 1, 3, and 16 distinct 3-chromatic simple graphs on 
,
4, and 5 nodes are illustrated above.
The 1 and 4 distinct 4-chromatic simple graphs on 
and 5 nodes
are illustrated above.
The following table gives the number of unlabeled simple graphs on 
, 2, ... nodes having specified
chromatic number 
.
 | OEIS | simple
graphs on  ,
2, ... nodes having  |
| 1 | A000012 | 1, 1, 1, 1, 1, 1, 1, ... |
| 2 | A076278 | 0, 1, 2, 6, 12, 34, 87, 302, 1118, ... |
| 3 | A076279 | 0, 0, 1, 3, 16, 84, 579, 5721, 87381, ... |
| 4 | A076280 | 0, 0, 0, 1, 4, 31, 318, 5366, 155291, ... |
| 5 | A076281 | 0, 0, 0, 0, 1, 5, 52, 867, 28722, ... |
| 6 | A076282 | 0, 0, 0, 0, 0, 1, 6, 81, 2028, ... |
| 7 | A076283 | 0, 0, 0, 0, 0, 0, 1, 7, 118, ... |
The triangle of numbers of graphs on 
nodes having chromatic
numbers 1, ..., 
is therefore given by 1; 1, 1; 1, 2, 1; 1, 6, 3, 1; 1, 12, ... (OEIS A084268).
The 1, 1, 3, and 5 connected 2-chromatic simple graphs on 
,
3, 4, and 5 nodes are illustrated above.
The 1, 2, and 12 connected 3-chromatic simple graphs on 
,
4, and 5 nodes are illustrated above.
The 1 and 3 connected 4-chromatic simple graphs on 
and 5 nodes are illustrated above.
The following table gives the number of unlabeled connected simple graphs
on 
,
2, ... nodes having specified chromatic
number 
.
 | OEIS | simple
connected graphs on  ,
2, ...nodes having  |
| 1 | 1, 0, 0, 0, 0, 0, ... | |
| 2 | A005142 | 0, 1, 1, 3, 5, 17, 44, 182, 730, ... |
| 3 | A126737 | 0, 0, 1, 2, 12, 64, 475, 5036, 80947, ... |
| 4 | A126738 | 0, 0, 0, 1, 3, 26, 282, 5009, 149551, ... |
| 5 | A126739 | 0, 0, 0, 0, 1, 4, 46, 809, 27794, ... |
| 6 | A126740 | 0, 0, 0, 0, 0, 1, 5, 74, 1940, ... |
| 7 | A241702 | 0, 0, 0, 0, 0, 0, 1, 6, 110, ... |
The triangle of numbers of connected simple graphs on 
nodes having chromatic
numbers 1, ..., 
is therefore given by 1; 0, 1; 0, 1, 1; 0, 3, 2, 1; 0, 5, 12, ... (OEIS A084269).
The 1, 6, and 40 labeled 2-chromatic simple graphs on 
,
3, and 4 nodes are illustrated above.
The 1 and 22 labeled 3-chromatic simple graphs on 
and 4 nodes are illustrated above.
The following table gives the number of labeled simple graphs on 
, 2, ... nodes having specified
chromatic number 
.
 | OEIS | labeled
simple graphs on  ,
2, ... nodes having  |
| 1 | 1, 1, 1, 1, 1, 1, ... | |
| 2 | A084270 | 0, 1, 6, 40, 375, 5176, ... |
| 3 | A084271 | 0, 0, 1, 22, 582, 22377, ... |
| 4 | A084272 | 0, 0, 0, 1, 65, 5042, ... |
| 5 | 0, 0, 0, 0, 1, 171, ... |
The 1, 3, and 19 labeled connected 2-chromatic simple graphs on 
, 3, and 4 nodes are illustrated
above.
The 1 and 18 labeled connected 3-chromatic simple graphs on 
and 4 nodes are illustrated
above.
The following table gives the number of labeled connected simple graphs
on 
,
2, ... nodes having specified chromatic
number 
.
, 2, ... nodes having 
-Colorings of a Graph on a Fixed Surface." Disc. Math. 306,
3145-3153, 2006.