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(2025) proposed a distance Laplacian analog of Brouwer's conjecture on partial sums of Laplacian eigenvalues, asserting that for any connected graph $G$, $\\sum_{i=1}^r \\partial_i^L(G)\\le W(G)+\\binom{r+2}{3},$ where $\\partial_i^L(G)$ are the eigenvalues of the distance Laplacian matrix and $W(G)$ is the Wiener index. We prove this inequality for three broad classes of graphs, thereby improving and extending existing results. First, we prove that all connected graphs of diameter at most $D$ satisfy the inequality once the order $n$ satisfies $n\\ge\\lceil\\frac49(D+1)^3\\rceil$. 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(2025) proposed a distance Laplacian analog of Brouwer's conjecture on partial sums of Laplacian eigenvalues, asserting that for any connected graph $G$, $\\sum_{i=1}^r \\partial_i^L(G)\\le W(G)+\\binom{r+2}{3},$ where $\\partial_i^L(G)$ are the eigenvalues of the distance Laplacian matrix and $W(G)$ is the Wiener index. We prove this inequality for three broad classes of graphs, thereby improving and extending existing results. First, we prove that all connected graphs of diameter at most $D$ satisfy the inequality once the order $n$ satisfies $n\\ge\\lceil\\frac49(D+1)^3\\rceil$. 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