# Self-adjointness of perturbed bi-Laplacians on infinite graphs

## TL;DR

This paper establishes a sufficient condition for the essential self-adjointness of perturbed bi-Laplacians on infinite graphs, extending previous results to unbounded degree functions and non-constant perturbations.

## Contribution

It provides a new criterion for self-adjointness of perturbed bi-Laplacians on infinite graphs, applicable to unbounded and non-constant perturbations.

## Key findings

- Criteria for essential self-adjointness of perturbed bi-Laplacians.
- Applicable to graphs with unbounded degree functions.
- Handles perturbations not bounded from below by a constant.

## Abstract

We give a sufficient condition for the essential self-adjointness of a perturbation of the square of the magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function is not necessarily bounded. The result allows perturbations that are not necessarily bounded from below by a constant.