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Let P(G,λ) be the chromatic polynomial of a simple graph G. A graph G is chromatically unique if for any simple graph H, P(H,λ) = P(G,λ) implies that H is isomorphic to G. Many sufficient conditions guaranteeing that some certain complete tripartite graphs are chromatically unique were obtained by many scholars. Especially, in 2003, Zou Hui-wen showed that if n 〉 1/3m2 + 3/1k2 + 3/1mk+ 1/3m-1/3k+ 3/2√m2 + k2 + mk, where n,k and m are non-negative integers, then the complete tripartite graph K(n - m,n,n + k) is chromatically unique (or simply χ–unique). In this paper, we prove that for any non-negative integers n,m and k, where m ≥ 2 and k ≥ 0, if n ≥ 3/1m2 + 3/1k2 + 3/1mk + 3/1m - 3/1k + 43, then the complete tripartite graph K(n - m,n,n + k) is χ–unique, which is an improvement on Zou Hui-wen’s result in the case m ≥ 2 and k ≥ 0. Furthermore, we present a related conjecture.  相似文献
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