Comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs

TL;DR

This paper compares Steklov and Laplacian eigenvalues on graphs, establishing inequalities and rigidity results, and applies these to derive estimates relevant to graph theory and spectral analysis.

Contribution

It introduces a comparison framework between Steklov and Laplacian eigenvalues on graphs, including rigidity results and applications to eigenvalue estimates.

Findings

Established comparison between Steklov and Laplacian eigenvalues.

Derived Lichnerowicz-type estimates for Steklov eigenvalues.

Provided combinatorial estimates for Steklov eigenvalues.

Abstract

In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs and discuss its rigidity. As applications of the comparison of eigenvalues, we obtain Lichnerowicz-type estimates and some combinatorial estimates for Steklov eigenvalues on graphs.