Signless Laplacian spectral characterization of some graphs

Abstract

In this paper, we investigate (signless) Laplacian spectral characterization of graphs with star components. Also, we prove that the join graph K n−α − e ∨ αK 1 is DQS for n − α > 3 and α = 3, and for α = 3, we show that its only Q-cospectral mate is K 1,3 ∪ K 2 ∪ (n − 6)K 1 .