On the Energy of Unitary Cayley Graphs

Abstract

In this note we obtain the energy of unitary Cayley graph $X_{n}$ which extends a result of R. Balakrishnan for power of a prime and also determine when they are hyperenergetic. We also prove that ${E(X_{n})\over 2(n-1)}\geq{2^{k}\over 4k}$, where $k$ is the number of distinct prime divisors of $n$. Thus the ratio ${E(X_{n})\over 2(n-1)}$, measuring the degree of hyperenergeticity of $X_{n}$, grows exponentially with $k$.