The least eigenvalue of signless Laplacian of non-bipartite graphs with given domination number

TL;DR

This paper establishes a lower bound for the smallest eigenvalue of the signless Laplacian in connected non-bipartite graphs based on their domination number, contributing to spectral graph theory.

Contribution

It provides a new lower bound for the least eigenvalue of the signless Laplacian in non-bipartite graphs with a given domination number, extending spectral bounds.

Findings

Lower bound for the least eigenvalue in terms of domination number

Applicable to connected non-bipartite graphs with specific domination constraints

Advances understanding of spectral properties related to domination number

Abstract

Let $G$ be a connected non-bipartite graph on $n$ vertices with domination number $\gamma \le \frac{n+1}{3}$. We investigate the least eigenvalue of the signless Laplacian of $G$, and present a lower bound for such eigenvalue in terms of the domination number $\gamma$.