Unit and unitary Cayley graphs for the ring of Gaussian integers modulo n

Abstract

Let Zn[i] be the ring of Gaussian integers modulo n and G(Zn[i]) and GZn[i] be the unit graph and the unitary Cayley graph of Zn[i], respectively. In this paper, we study G(Zn[i]) and GZn[i]. Among many results, it is shown that for each positive integer n, the graphs G(Zn[i]) and GZn[i] are Hamiltonian. We also nd a necessary and sucient condition for the unit and unitary Cayley graphs of Zn[i] to be Eulerian.