Laplacian spectrum of comaximal graph of the ring ℤ n

Abstract In this paper, we study the interplay between the structural and spectral properties of the comaximal graph Γ (Z n) ({Z}₍) of the ring Z n {Z}₍ for n > 2 n 2. We first determine the structure of Γ (Z n) ({Z}₍) and deduce some of its properties. We then use the structure of Γ (Z n) ({Z}₍) to deduce the Laplacian eigenvalues of Γ (Z n) ({Z}₍) for various n n. We show that Γ (Z n) ({Z}₍) is Laplacian integral for n = p α q β n=p^ q^, where p, q p, q </jats: