For a connected graph G and $\alpha \in [0,1)$, the distance α-spectral radius of G is the spectral radius of the matrix $D_{\alpha }(G)$ defined as $D_{\alpha }(G)=\alpha T(G)+(1-\alpha )D(G)$, where $T(G)$ is a diagonal matrix of vertex transmissions of G and $D(G)$ is the distance matrix of G. We give bounds for the distance α-spectral radius, especially for graphs that are not transmission regular, propose local graft transformations that decrease or increase the distance α-spectral radius, and determine the graphs that minimize and maximize the distance α-spectral radius among several families of graphs.

中文翻译：

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关于连通图的距离α-光谱半径

对于一个连通图G和[\​​，1] $中的\\ alpha \，距离G的光谱半径是定义为$ D _ {\ alpha的矩阵$ D _ {\ alpha}（G）$的光谱半径}（G）= \ alpha T（G）+（1- \ alpha）D（G）$，其中$ T（G）$是G顶点传输的对角矩阵，$ D（G）$是距离我们给距离α谱半径定界，尤其是对于那些不具有透射规律的图，提出减小或增加距离α谱半径的局部嫁接变换，并确定最小化和最大化距离α的图几族图形之间的光谱半径。