About chromatic uniqueness of some complete tripartite graphs

Let $P(G,x)$ be the chromatic polynomial of a graph $G$. A graph $G$ is called $\mathit{\text{chromatically}}\mathit{\text{unique}}$ if for any graph $H,P(G,x)=P(H,x)$ implies that $G$ and $H$ are isomorphic. In this paper we show that full tripartite graph $K(n_1,n_2,n_3)$ is chromatically unique if $n_1 \geq n_2 \geq n_2 \geq n_3 \geq 2, n_1 - n_3 \leq 5$and$n_1 + n_2 + n_3 \not \equiv 2 \mod{3}$.