New bounds on the distance Laplacian and distance signless Laplacian spectral radii

TL;DR

This paper establishes new bounds on the spectral radii of the distance Laplacian and distance signless Laplacian matrices of graphs, with some bounds being sharp and characterized by specific graph structures.

Contribution

It introduces novel upper bounds for the distance Laplacian spectral radius and both lower and upper bounds for the distance signless Laplacian spectral radius, including characterizations of extremal graphs.

Findings

New upper bounds for the distance Laplacian spectral radius

New lower and upper bounds for the distance signless Laplacian spectral radius

Characterization of graphs attaining the bounds

Abstract

Let G be a simple undirected connected graph. In this paper, new upper bounds on the distance Laplacian spectral radius of G are obtained. Moreover, new lower and upper bounds for the distance signless Laplacian spectral radius of G are derived. Some of the above mentioned bounds are sharp and the graphs attaining the corresponding bound are characterized. Several illustrative examples are included.