For a simple graph G on n vertices, the signless Laplacian Estrada index is defined as SLEE(G) = n i=1 e q i , where q 1 , q 2 , . . . , q n are the eigenvalues of the signless Laplacian matrix of G. In this paper, the unique graph on n vertices with maximum signless Laplacian Estrada index is determined among graphs with given number of cut edges, pendent vertices, (vertex) connectivity and edge connectivity, respectively.

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 edges, pendent vertices, (vertex) connectivity and edge connectivity. In this paper we continue our charachterization for two further parameters; diameter and number of cut vertices.

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