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Bounds of eigenvalues of a graph

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Abstract

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.

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  1. East China Normal University, China

    Hong Yuan

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  1. Hong Yuan
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Hong, Y. Bounds of eigenvalues of a graph. Acta Mathematicae Applicatae Sinica 4, 165–168 (1988). https://doi.org/10.1007/BF02006065

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  • DOI: https://doi.org/10.1007/BF02006065

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