# Laplacian Spectrum of non-commuting graphs of finite groups

## TL;DR

This paper computes the Laplacian spectrum of non-commuting graphs for certain finite groups, showing they are L-integral and establishing conditions for this property.

## Contribution

It provides explicit spectral computations for non-commuting graphs of specific finite groups and identifies conditions for their L-integrality.

## Key findings

- Non-commuting graphs of studied groups are L-integral
- Spectral properties depend on group structure
- Conditions for L-integrality of non-commuting graphs

## Abstract

In this paper, we compute the Laplacian spectrum of non-commuting graphs of some classes of finite non-abelian groups. Our computations reveal that the non-commuting graphs of all the groups considered in this paper are L-integral. We also obtain some conditions on a group $G$ so that its non-commuting graph is L-integral.