Erratum to "A note on the largest eigenvalue of non-regular graphs"

Abstract

Let λ₁(G) be the largest eigenvalue of the adjacency matrix of graph G with n vertices and maximum degree ∆. Recently, ∆ −λ₁(G) > ∆+1/n(3n+∆−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. Bııyıko˘glu 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. Bııyıko˘glu and J. Leydold]