Some relations between power graphs and Cayley graphs

Motivated by an open problem of Abawajy et al. [1] we find some relations between power graphs and Cayley graphs of finite cyclic groups. We show that the vertex deleted subgraphs of some power graphs are spanning subgraphs or equal to the complement of vertex deleted subgraphs of some unitary Cayley graphs. Also we prove that some Cayley graphs can be expressed as direct product of power graphs. Applying these relations we study the eigenvalues and energy of power graphs and the related Cayley graphs.