Signless Laplacian spectrum of power graphs of finite cyclic groups

Abstract

In this paper, we have studied Signless Laplacian spectrum of the power graph of finite cyclic groups. We have showed that n−2 is an eigen value of Signless Laplacian of the power graph of Zn,n≥2 with multiplicity at least ϕ(n). In particular, using the theory of Equitable Partitions, we have completely determined the Signless Laplacian spectrum of power graph of Zn for n=pq where p,q are distinct primes.