The signless Laplacian Estrada index of tricyclic graphs

Abstract

The signless Laplacian Estrada index of a graph $G$ is defined as $SLEE(G)={\sum }_{i=1}^n{e}^{q_i}$ where $q_1,q_2,\dots ,q_n$ 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.

12 pages, 4 figures