Signless Laplacian spectral radius for a k-extendable graph

Let k and n be two nonnegative integers with n equivalent to 0 (mod 2), and let G be a graph of order n with a perfect matching. Then G is said to be k-extendable for 0 <= k <= n-2/2 if every matching in G of size k can be extended to a perfect matching. In this paper, we first establish a lower bound on the signless Laplacian spectral radius of G to ensure that G is k-extendable. Then we create some extremal graphs to claim that all the bounds derived in this article are sharp.