Erratum to "A note on the largest eigenvalue of non-regular graphs"
Erratum to "A note on the largest eigenvalue of non-regular graphs"
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DOI：
10.13001/1081-3810.1294
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发表时间：
2009
影响因子：
0.7
通讯作者：
Bolian Liu;Liu Mu-huo;Zhifu You
中科院分区：
文献类型：
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作者：
Bolian Liu;Liu Mu-huo;Zhifu You
设λ1(G)是图G的n个顶点的最大度∆的邻接矩阵的最大特征值。最近，非正则连通图G的∆−λ1(G)>；∆+1n(3n+∆−8)在[B.L.Liu，G.Li，关于非正则图的最大特征值的注记，线性代数，17：54-61,2008]中得到。但遗憾的是，在引用的预印本[T.Biiyi koglu和J.Leydold，度序列的最大特征值]中发现了一个错误，导致了对[B.L.Liu和G.Li]的主要结果的错误证明。本文对[B.L.Liu和G.Li]中的主要结果给出了正确的证明，避免了[T.Biiyi koglu和J.Leydold]中的错误定理。
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. Biiyikoglu 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. Biiyikoglu and J. Leydold].