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 M₁₁, 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_4n), where Dic_4n is the dicyclic group, we finally give bounds on the signless Laplacian spectral radius.