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Many open quipus and closed quipus have spectral radius greater than $3/2{\\sqrt{2}}$. In this paper we proved the following results. For any open quipu $G$ on $n$ vertices ($n\\geq 6$) with spectral radius less than $3/2{\\sqrt{2}}$, its diameter $D(G)$ satisfies $D(G)\\geq (2n-4)/3$. This bound is tight. 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