The distance Laplacian spectral radius of unicyclic graphs

TL;DR

This paper identifies the unicyclic graphs that have the maximum distance Laplacian spectral radius, advancing understanding of spectral properties related to graph structure.

Contribution

It determines the unique unicyclic graphs with the maximum distance Laplacian spectral radius, a novel spectral extremal result.

Findings

Identified the unicyclic graphs with maximum spectral radius

Provided a characterization of these extremal graphs

Enhanced understanding of spectral graph theory for unicyclic graphs

Abstract

For a connected graph $G$, the distance Laplacian spectral radius of $G$ is the spectral radius of its distance Laplacian matrix $\mathcal{L}(G)$ defined as $\mathcal{L}(G)=Tr(G)-D(G)$, where $Tr(G)$ is a diagonal matrix of vertex transmissions of $G$ and $D(G)$ is the distance matrix of $G$. In this paper, we determine the unique graphs with maximum distance Laplacian spectral radius among unicyclic graphs.