The distance Laplacian matrix of a connected graph G is defined as $\mathcal{L}\left(G\right)=Tr\left(G\right)-D\left(G\right)$, where $Tr\left(G\right)$ is the diagonal matrix of the vertex transmissions in G and $D\left(G\right)$ is the distance matrix of G. The largest eigenvalue of $\mathcal{L}\left(G\right)$ is called the distance Laplacian spectral radius of G. In this paper, we determine the graphs with the maximum distance Laplacian spectral radius and the minimum distance Laplacian spectral radius among all the bicyclic graphs with given order, respectively.

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关于双环图的距离拉普拉斯谱半径

连通图G的距离拉普拉斯矩阵定义为$\mathcal{大号}（G）=Ť\mathrm{[R}（G）-d（G）$， 在哪里 $Ť\mathrm{[R}（G）$是在顶点传输的对角矩阵G ^和$d（G）$是G的距离矩阵。的最大特征值$\mathcal{大号}（G）$称为G的距离拉普拉斯光谱半径。在本文中，我们确定了所有双环图中具有给定阶数的最大距离拉普拉斯谱半径和最小距离拉普拉斯谱半径的图。