  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 vertices, (vertex) connectivity and edge
connectivity. In this paper we continue out characterization for two further
parameters; diameter and number of cut vertices.
