图的$A_\alpha$谱半径的注释

A Note on the $A_{\alpha}$-Spectral Radius of a Graph

中文关键词:  图  $A_\alpha$谱半径  主特征向量

英文关键词:graph  $A_{\alpha}$-spectral radius  Principal eigenvector

中文摘要:

      设$G$为具有$n$个顶点的简单图, $\rho_\alpha(G)$为其$A_\alpha(G)$谱半径.对图$G$的任一顶点$v_i$, 本文给出了$\rho_\alpha(G)$与$\rho_alpha(G-v_i)$之间的关系.

英文摘要:

      Let $G$ be a simple graph of order $n$ and $\rho_{\alpha}(G)$ be the $A_{\alpha}(G)$-spectral radius of $G$. In this note, for any vertex $v_i$ of $G$, we establish the relationship between $\rho_{\alpha}(G)$ and $\rho_{\alpha}(G-v_i)$.