Some Lower Bounds on the Spectral Radius of Graphs

Xu Yang1, Jiang Weixin2, Chen Cang2
1College of Sciences, Laiyang Agricultural College, Qing Dao, Shandong 266109, China
2College of Sciences, China University of Mining and Technology, Xu Zhou, Jiangsu 221008, China

Abstract

Let \(G\) be a simple connected graph. The spectral radius \(\rho(G)\) of \(G\) is the largest eigenvalue of its adjacency matrix. In this paper, we obtain two lower bounds of \(\rho(G)\) by two different methods, one of which is better than another in some conditions.