Chromatic polynomial determines a Turán graph
= Chromatic polynomial determines a Turán graph
For integers $1\leq r\leq n$, if a simple graph has the same <chromatic polynomial> as the <Turán graph> $T_r(n)$, it has the same number of vertices and edges, and the same <chromatic number> $r$. It is therefore $K_{r+1}$-free and attains equality in <Turán's theorem>. The equality case forces it to be isomorphic to $T_r(n)$.