A Note on the $A_{\alpha}$-Spectral Radius of a Graph
Received:January 04, 2022  Revised:May 08, 2022
Key Words: graph   $A_{\alpha}$-spectral radius   Principal eigenvector
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12171089) and the Natural Science Foundation of Fujian Province (Grant No.2021J02048).
 Author Name Affiliation Hongzhang CHEN School of Mathematics and Statistics, Minnan Normal University, Fujian 363000, P. R. China Jianxi LI School of Mathematics and Statistics, Minnan Normal University, Fujian 363000, P. R. China
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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 $\rho_{\alpha}(G-v_i)$.