Let $G=(V\left(G\right),E\left(G\right))$ be a weighted digraph with vertex set $V\left(G\right)=\{v_1,v_2,\dots ,v_n\}$ and arc set $E\left(G\right)$, where the arc weights are nonzero nonnegative symmetric matrices. In this paper, we obtain an upper bound on the signless Laplacian spectral radius of a weighted digraph $G$, and if $G$ is strongly connected, we also characterize the digraphs achieving the upper bound. Moreover, we show that an upper bound of weighted digraphs or unweighted digraphs can be deduced from our upper bound.

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关于加权有向图的无符号拉普拉斯谱半径

让 $G=（V（G），Ë（G））$ 是带有顶点集的加权有向图 $V（G）=\{v_{\mathrm{1个}}，v_2，\dots ，v_{ñ}\}$ 和弧集 $Ë（G）$，其中弧权重为非零非负对称矩阵。在本文中，我们获得了加权有向图的无符号拉普拉斯谱半径的上限$G$， 而如果 $G$是紧密相连的，我们还描述了有向图达到上限的图。此外，我们表明可以从我们的上限推导加权图或未加权图的上限。