A NOTE ON THE LARGEST EIGENVALUE OF NON-REGULAR GRAPHS (vol 17, pg 54, 2008)

作者：Liu, Bolian^*; Mu Huo, Liu; You, Zhifu

来源：Electronic Journal of Linear Algebra, 2009, 18: 64-68.

• Spectral radius
• Non-regular graph
• lambda(1)-extremal graph
• Perron vector

Let lambda(1)(G) be the largest eigenvalue of the adjacency matrix of graph G with n vertices and maximum degree Delta. Recently, Delta - lambda(1)(G) > Delta 1/n(3n Delta-8) for a non-regular connected graph G was obtained in [B. L. Liu and G. Li, A note on the largest eigenvalue of non-regular graphs, Electron J. Linear Algebra, 17:54-61, 2008]. But unfortunately, a mistake was found in the cited preprint [T. Buyikoglu and J. Leydold, Largest eigenvalues of degree sequences], which led to an incorrect proof of the main result of [B. L. Liu and G. Li]. This paper presents a correct proof of the main result in [B. L. Liu and G. Li], which avoids the incorrect theorem in [T. Biiyiko. glu and J. Leydold].

• 出版日期2009-1
• 单位华南师范大学; 华南农业大学