First eigenvalue estimates of Dirichlet-to-Neumann operators on graphs

TL;DR

This paper introduces new isoperimetric constants for finite graphs with boundary and provides lower bounds for the first nontrivial eigenvalues of Dirichlet-to-Neumann operators, extending previous work on eigenvalue estimates.

Contribution

It proposes two novel types of isoperimetric constants and establishes lower bound estimates for eigenvalues on finite graphs, advancing spectral graph theory.

Findings

Two new isoperimetric constants are defined.

Lower bounds for eigenvalues are derived.

Results extend previous eigenvalue estimation methods.

Abstract

Following Escobar [Esc97] and Jammes [Jam15], we introduce two types of isoperimetric constants and give lower bound estimates for the first nontrivial eigenvalues of Dirichlet-to-Neumann operators on finite graphs with boundary respectively.