The signless Laplacian Estrada index of tricyclic graphs

TL;DR

This paper identifies the two tricyclic graphs with the highest signless Laplacian Estrada index, contributing to spectral graph theory by characterizing extremal structures for this index.

Contribution

It determines the exact extremal tricyclic graphs with maximal signless Laplacian Estrada index, a novel result in spectral graph theory.

Findings

Two tricyclic graphs have the maximal signless Laplacian Estrada index.

Characterization of extremal graphs for the SLEE among tricyclic graphs.

Advances understanding of spectral properties of complex graphs.

Abstract

The signless Laplacian Estrada index of a graph $G$ is defined as $SLEE(G)=\sum^{n}_{i=1}e^{q_i}$ where $q_1, q_2, \ldots, q_n$ are the eigenvalues of the signless Laplacian matrix of $G$. In this paper, we show that there are exactly two tricyclic graphs with the maximal signless Laplacian Estrada index.