Signless Laplacian spectrum of power graph of certain finite non-commutative groups

In this present study, we investigate the signless Laplacian spectrum of power graphs of different finite non-commutative groups. Initially, we obtain the spectrum of the signless Laplacian matrix of power graph of elementary abelian groups whose orders are powers of a prime number. The signless Laplacian spectrum of the smallest sporadic group, the Mathieu group M 11 , is then computed. We also find the signless Laplacian eigenvalues of 𝒫( Q 2 k +2 ), where Q 2 k +2 represents the generalized quaternion group. For 𝒫(Dic 4 n ), where Dic 4 n is the dicyclic group, we finally give bounds on the signless Laplacian spectral radius.