On Maximum Signless Laplacian Estrada Indices of Graphs with Given Parameters

Abstract

Signless Laplacian Estrada index of a graph $G$, defined as $SLEE(G)={\sum }_{i=1}^n{e}^{q_i}$, 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.

14 pages, 3 figures