In this paper, we obtain the eigenvalues and Laplacian eigenvalues of the unitary addition Cayley graph G n and its complement. Moreover, we compute the bounds for energy and Laplacian energy for G n and its complement. 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 the complement of G n is hyperenergetic if and only if n has at least two distinct prime factors and n 2p.
For a positive integer n > 1, the unitary addition Cayley graph G n is the graph whose vertex set is V (G n ) = Z n = {0, 1, 2, · · · , n − 1} and the edge set E(G n ) = {ab | a, b ∈ Z n , a + b ∈ U n } where U n = {a ∈ Z n | gcd(a, n) = 1}. For G n the independence number, chromatic number, edge chromatic number, diameter, vertex connectivity, edge connectivity and perfectness are determined.
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