On the Line Graph of the Zero Divisor Graph for the Ring of Gaussian Integers Modulo n

Let be the zero divisor graph for the ring of the Gaussian integers modulo . Several properties of the line graph of , are studied. It is determined when is Eulerian, Hamiltonian, or planer. The girth, the diameter, the radius, and the chromatic and clique numbers of this graph are found. In addition, the domination number of is given when is a power of a prime. On the other hand, several graph invariants for are also determined.