A note on limit of first eigenfunctions of p-Laplacian on graphs

2018/12/19 by Huabin Ge, Bobo Hua, Ge, Huabin +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1812.07915

Abstract

We study the limit of first eigenfunctions of (discrete) p-Laplacian on a finite subset of a graph with Dirichlet boundary condition, as p→ 1. We prove that up to a subsequence, they converge to a summation of characteristic functions of Cheeger cuts of the graph. We give an example to show that the limit may not be a characteristic function of a single Cheeger cut.

Citations

• q-Difference Equations

Cited by

• Geometric and spectral properties of directed graphs under a lower Ricci curvature bound

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