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LetG be a simple graph withn vertices. We denote by λi(G) thei-th largest eigenvalue ofG. In this paper, several results are presented concerning bounds on the eigenvalues ofG. In particular, it is shown that −1⩽λ2(G)⩽(n−2)/2, and the left hand equality holds if and only ifG is a complete graph with at least two vertices; the right hand equality holds if and only ifn is even andG℞2K n/2.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 13, 2005
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