On Laplacian spectrum of unitary Cayley graphs

Let R be a commutative ring with unity 1 ≠ 0 and let R^× be the set of all unit elements of R. The unitary Cayley graph of R, denoted by G_R = Cay(R, R^×), is a simple graph whose vertex set is R and there is an edge between two distinct vertices x and y of R if and only if x − y ∈ R^×. In this paper, we determine the Laplacian and signless Laplacian eigenvalues for the unitary Cayley graph of a commutative ring. Also, we compute the Laplacian and signless Laplacian energy of the graph G_R and its line graph.