On the difference between the spectral radius and the maximum degree of graphs

• Date: 2018
• Main Author: Oboudi, Mohammad Reza
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: tree; eigenvalues of graphs; spectral radius of graphs; maximum degree; 05C31; 05C50; 15A18
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/303
• Journal Title: Algebra and Discrete Mathematics

Let \(G\) be a graph with the eigenvalues \(\lambda_1(G)\geq\cdots\geq\lambda_n(G)\). The largest eigenvalue of \(G\), \(\lambda_1(G)\), is called the spectral radius of \(G\). Let \(\beta(G)=\Delta(G)-\lambda_1(G)\), where \(\Delta(G)\) is the maximum degree of vertices of \(G\). It is known that i...