The second least eigenvalue of the signless Laplacian of the complements of trees

Suppose that Tnc is a set, such that the elements of Tnc are the complements of trees of order n. In 2012, Li and Wang gave the unique graph in the set Tnc ∖ {K1, n − 1c} with minimum 1st ‘least eigenvalue of the signless Laplacian’ (abbreviated to a LESL). In the present work, we give the unique graph with 2nd LESL in Tnc ∖ {K1, n − 1c}, where K1, n − 1c represents the complement of star of order n.