Essential self-adjointness for combinatorial Schr\"odinger operators II- Metrically non complete graphs

TL;DR

This paper investigates the essential self-adjointness of weighted graph Laplacians and Schr"odinger operators on metrically non-complete graphs, expanding understanding of their spectral properties in non-complete metric settings.

Contribution

It extends previous work by analyzing essential self-adjointness for operators on non-complete weighted graphs with a metric structure.

Findings

Conditions for essential self-adjointness in non-complete graphs

Characterization of spectral properties of graph operators in non-complete settings

New criteria for self-adjointness based on weighted metric structures

Abstract

We consider weighted graphs, we equip them with a metric structure given by a weighted distance, and we discuss essential self-adjointness for weighted graph Laplacians and Schr\"odinger operators in the metrically non complete case.