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

الملخص EN

Let Γ(ℤn[i]) be the zero divisor graph for the ring of the Gaussian integers modulo n.

Several properties of the line graph of Γ(ℤn[i]), L(Γ(ℤn[i])) are studied.

It is determined when L(Γ(ℤn[i])) 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 L(Γ(ℤn[i])) is given when n is a power of a prime.

On the other hand, several graph invariants for Γ(ℤn[i]) are also determined.