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

Muhammad Ajmal, Masood Ur Rehman, Tayyab Kamran

Abstract


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.


Keywords


eigenvalue, tree, signless Laplacian matrix

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DOI: http://dx.doi.org/10.5614/ejgta.2019.7.2.6

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ISSN: 2338-2287

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