Bounds for Generalized Distance Spectral Radius and the Entries of the Principal Eigenvector
Bounds for Generalized Distance Spectral Radius and the Entries of the Principal Eigenvector
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DOI：
10.5556/j.tkjm.52.2021.3280
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发表时间：
2021-01
影响因子：
0.6
通讯作者：
Hilal Ahmad;A. Alhevaz;M. Baghipur;Gui-Xian Tian
中科院分区：
文献类型：
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作者：
Hilal Ahmad;A. Alhevaz;M. Baghipur;Gui-Xian Tian
对于简单连通图$G$，定义$Tr(G)$和$D(G)$的凸线性组合$D_{\alpha}(G)$为$D_{\alpha}(G)=\alpha Tr(G)+(1-\alpha)D(G)$, $0\leq \alpha\leq 1$。作为$D_{0}(G)=D(G)$, $2D_{\frac{1}{2}}(G)=D^{Q}(G)$, $D_{1}(G)=Tr(G)$和$D_{\alpha}(G)-D_{\beta}(G)=(\alpha-\beta)D^{L}(G)$，该矩阵简化为合并距离谱和距离无符号拉普拉斯谱理论。本文研究广义距离矩阵$D_{\alpha}(G)$的谱性质。我们得到了涉及不同图参数的广义距离谱半径的下界和上界，并对极值图进行了刻画。进一步，我们得到了广义距离矩阵$D_{\alpha}(G)$的谱半径$ \partial(G) $对应的$ p $ -范数归一化Perron向量的最大值和最小值的上界和下界，并刻画了极值图。
For a simple connected graph $G$, the convex linear combinations $D_{\alpha}(G)$ of \ $Tr(G)$ and $D(G)$ is defined as $D_{\alpha}(G)=\alpha Tr(G)+(1-\alpha)D(G)$, $0\leq \alpha\leq 1$. As $D_{0}(G)=D(G)$, $2D_{\frac{1}{2}}(G)=D^{Q}(G)$, $D_{1}(G)=Tr(G)$ and $D_{\alpha}(G)-D_{\beta}(G)=(\alpha-\beta)D^{L}(G)$, this matrix reduces to merging the distance spectral and distance signless Laplacian spectral theories. In this paper, we study the spectral properties of the generalized distance matrix $D_{\alpha}(G)$. We obtain some lower and upper bounds for the generalized distance spectral radius, involving different graph parameters and characterize the extremal graphs. Further, we obtain upper and lower bounds for the maximal and minimal entries of the $ p $-norm normalized Perron vector corresponding to spectral radius $ \partial(G) $ of the generalized distance matrix $D_{\alpha}(G)$ and characterize the extremal graphs.