Suppose $c(G,u)$ is chromatic polynomial of connected simple graph $G$. We know that $|c(G,-1)|$, as Stanley proved, is the total number of directed graph on $G$, without any cycle. Also, we know ...
Does anyone know more examples of two nonisomorphic connected graphs with the same chromatic symmetric function? The only pair I know is the one in Stanley's paper on c.s.f.'s ...