Let G be a connected graph, we define $D^Q(G)=Tr(G)+D(G)$ as distance signless Laplacian matrix of G, where $Tr(G)$ and $D(G)$ are diagonal matrix with vertex transmissions of G and distance matrix of G, respectively. In this paper, we characterize the extremal graphs which maximize the $D^Q$-spectral radius among complements of unicyclic graphs and trees, respectively. And we also characterize the unique graph among complements of unicyclic graphs of diameter three which maximize the least $D^Q$-eigenvalues.

中文翻译：

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关于单环图和树的补集的距离无符号拉普拉斯谱

令G为连通图，我们定义$D^{问}(G)=吨r(G)+D(G)$作为G 的距离无符号拉普拉斯矩阵，其中$吨r(G)$ 和 $D(G)$与顶点传输对角矩阵G ^和的距离矩阵G ^分别。在本文中，我们描述了最大化$D^{问}$- 分别为单环图和树的补充之间的谱半径。并且我们还刻画了直径为 3 的单环图的补集之间的唯一图，该图最大化最小$D^{问}$- 特征值。