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On the distance α-spectral radius of a connected graph
Journal of Inequalities and Applications ( IF 1.5 ) Pub Date : 2020-06-11 , DOI: 10.1186/s13660-020-02427-4
Haiyan Guo , Bo Zhou

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:

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。
更新日期:2020-06-11
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