Let 
denote the chromatic polynomial of a finite
simple graph 
.
Then 
is said to be chromatically unique if 
implies that 
and 
are isomorphic graphs,
in other words, if 
is determined by its chromatic polynomial. If 
and 
are nonisomorphic but share the same chromatic
polynomial, they are said to be chromatically
equivalent.
Cycle graphs are chromatically unique (Chao and Whitehead 1978), as are Turán graphs (Chao and Novacky 1982).
Named graphs that are chromatically nonunique include the 3- and 4-barbell graph, bislit cube, bull graph, claw graph, 3-matchstick graph, Moser spindle, 2-Sierpiński gasket graph, star graphs, triakis tetrahedral graph, and 6- and 8-wheel graphs.
The numbers of chromatically nonunique simple graphs on 
nodes for 
, 2, ... are 0, 0, 0, 4, 18, 115, 905, 11642, 267398, ...
(OEIS A137567), while the corresponding numbers
of chromatically unique graphs are 1, 2, 4, 7, 16, 41, 139, 704, 7270, ... (OEIS
A137568).
-Colorable
and Chromatically Equivalent Graphs." Bull. Malays. Math. Sci. Soc. 24,
3-103, 2001.Chao, C.-Y.; Guo, Z. Y.; and Li, N. Z. "Some
Families of Chromatically Equivalent Graphs." Bull. Malays. Math. Soc. 15,
77-82, 1992.Chao, C.-Y.; Guo, Z.-Y.; Li, N.-Z. "On 
-Graphs. Chromatic Polynomials and Related Topics (Shanghai,
1994)." Discr. Math. 172, 9-16, 1997.Chao, C. Y.
and Novacky, G. A. "On Maximally Saturated Graphs." Disc. Math. 41,
139-143, 1982.Chao, C. Y. and Whitehead, E. G. Jr. "On
Chromatic Equivalence of Graphs." In 
-Polynomials."
J. Graph Th. 11, 169-176, 1987.Sloane, N. J. A.
Sequences