Bounds on the $A_{\alpha}$-spectral radius of a $C_3$-free graph
Bounds on the $A_{\alpha}$-spectral radius of a $C_3$-free graph
Received:October 04, 2020  Revised:October 04, 2020
DOI:
中文关键词:  
英文关键词:$C_3$-free graph  $k$-cycle graph  $A_{\alpha}$-spectral radius
基金项目:
Author NameAffiliationAddress
Shu-Guang Guo Yancheng Teachers University 江苏省盐城市开放大道50号 盐城师范学院 数学与统计学院
Dong-Xia Zhu Yancheng Teachers University 江苏省盐城市开放大道50号 盐城师范学院 数学与统计学院
Rong Zhang Yancheng Teachers University 江苏省盐城市开放大道50号 盐城师范学院 数学与统计学院
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中文摘要:
      
英文摘要:
      Let $G$ be a simple undirected graph. For any real number $\alpha \in[0,1]$, Nikiforov defined the $A_{\alpha}$-matrix of $G$ as $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$ in 2017, where $A(G)$ and $D(G)$ are the adjacency matrix and the degree diagonal matrix of $G$ respectively. In this paper, we obtain a lower bound on the $A_{\alpha}$-spectral radius of a $C_3$-free graph for $\alpha \in[0, 1)$ and a sharp upper bound on the $A_{\alpha}$-spectral radius of a $C_3$-free $k$-cycle graph for $\alpha \in[1/2, 1)$.
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