On Maximum Signless Laplacian Estrada Index of Graphs with Given Parameters II

TL;DR

This paper characterizes the graphs with maximum signless Laplacian Estrada index (SLEE) given parameters like diameter and number of cut vertices, extending previous work on other parameters.

Contribution

It provides new characterizations of graphs with maximum SLEE for diameter and cut vertices, advancing understanding of spectral graph properties.

Findings

Identified graphs with maximum SLEE for given diameter.

Determined graphs with maximum SLEE for a specified number of cut vertices.

Abstract

Recently Ayyaswamy [1] have introduced a novel concept of the signless Laplacian Estrada index (after here $SLEE$) associated with a graph $G$. After works, we have identified the unique graph with maximum $SLEE$ with a given parameter such as: number of cut vertices, (vertex) connectivity and edge connectivity. In this paper we continue out characterization for two further parameters; diameter and number of cut vertices.