Energy and Laplacian Energy of Unitary Addition Cayley Graphs

Abstract

In this paper, we obtain the eigenvalues and Laplacian eigenvalues of unitary
addition Cayley graph G_{n} and their complements. Moreover, we compute the
bounds for energy and Laplacian energy for G_{n} and their complements. In
addition, we prove that G_{n} is hyperenergetic if and only if n is odd other than
the prime number and power of 3 or n is even and has at least three distinct
prime factors. It is also shown that complement of G_{n} is hyperenergetic if and
only if n has at least two distinct prime factors and n not equal to 2p.