On Maximum Signless Laplacian Estrada Indices of Graphs with Given Parameters

TL;DR

This paper identifies the graphs with the highest signless Laplacian Estrada index within classes defined by specific parameters like cut edges, pendent vertices, and connectivity, advancing spectral graph theory understanding.

Contribution

It determines the unique extremal graphs with maximum SLEE for various graph classes constrained by structural parameters.

Findings

Identified graphs with maximum SLEE for given cut edges.

Determined extremal graphs for specified pendent vertices.

Established maximum SLEE graphs under connectivity constraints.

Abstract

Signless Laplacian Estrada index of a graph $G$, defined as $SLEE(G)=\sum^{n}_{i=1}e^{q_i}$, where $q_1, q_2, \cdots, q_n$ are the eigenvalues of the matrix $\mathbf{Q}(G)=\mathbf{D}(G)+\mathbf{A}(G)$. We determine the unique graphs with maximum signless Laplacian Estrada indices among the set of graphs with given number of cut edges, pendent vertices, (vertex) connectivity and edge connectivity.