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

Muhammad Ajmal (School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China)
Masood Ur Rehman (School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China)
Tayyab Kamran (Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 7, No 2 (2019): Electronic Journal of Graph Theory and Applications

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.