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Characterization of Graphs with an Eigenvalue of Large Multiplicity

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  • Linming Qi
  • Lianying Miao
  • Weiliang Zhao
  • Lu Liu

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.

Suggested Citation

  • Linming Qi & Lianying Miao & Weiliang Zhao & Lu Liu, 2020. "Characterization of Graphs with an Eigenvalue of Large Multiplicity," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:3054672
    DOI: 10.1155/2020/3054672
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    References listed on IDEAS

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    1. van Dam, E.R., 1997. "Nonregular Graphs with Three Eigenvalues," Research Memorandum 746, Tilburg University, School of Economics and Management.
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