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Let $G$ be a connected graph on $n$ vertices, and let $D(G)$ be the distance matrix of $G$. Let $\partial_1(G)\ge\partial_2(G)\ge\cdots\ge\partial_n(G)$ denote the eigenvalues of $D(G)$. In this paper, the connected graphs with @nô1(G) at least the smallest root of $x^3=3x^2-11x-6 = 0$ are determined. Additionally, some non-isomorphic distance cospectral graphs are given.