Characterization of Graphs with an Eigenvalue of Large Multiplicity

Linming Qi, Lianying Miao, Weiliang Zhao and Lu Liu

Advances in Mathematical Physics, 2020, vol. 2020, issue 1

Abstract: Let G be a simple and undirected graph. The eigenvalues of the adjacency matrix of G are called the eigenvalues of G. In this paper, we characterize all the n‐vertex graphs with some eigenvalue of multiplicity n − 2 and n − 3, respectively. Moreover, as an application of the main result, we present a family of nonregular graphs with four distinct eigenvalues.

Date: 2020
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https://doi.org/10.1155/2020/3054672

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:3054672

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