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<p>In this paper, we obtain some comparisons of the Dirichlet, Neumann and Laplacian eigenvalues on graphs. We also discuss their rigidities and some of their applications including some Lichnerowicz-type, Fiedler-type and Friedman-type estimates for Dirichlet eigenvalues and Neumann eigenvalues. The comparisons on Neumann eigenvalues can be translated as comparisons on Steklov eigenvalues in our setting. So, some of the results can be viewed as extensions for parts of [<CitationRef CitationID="CR11">11</CitationRef>] by Hua-Huang-Wang, and parts of our previous works [<CitationRef CitationID="CR20">20</CitationRef>, <CitationRef CitationID="CR21">21</CitationRef>].</p>

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Comparisons of Dirichlet, Neumann and Laplacian eigenvalues on graphs and their applications

  • 期刊论文

  • 发表日期：

    2025年10月18日

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  • Yongjie Shi,
  • Chengjie Yu

摘要

In this paper, we obtain some comparisons of the Dirichlet, Neumann and Laplacian eigenvalues on graphs. We also discuss their rigidities and some of their applications including some Lichnerowicz-type, Fiedler-type and Friedman-type estimates for Dirichlet eigenvalues and Neumann eigenvalues. The comparisons on Neumann eigenvalues can be translated as comparisons on Steklov eigenvalues in our setting. So, some of the results can be viewed as extensions for parts of [11] by Hua-Huang-Wang, and parts of our previous works [20, 21].