Zero Divisor Graph for the Ring of Gaussian Integers Modulon

On the Zero Divisor Graphs of the Ring of Lipschitz Integers Modulo n

“…Nevertheless, particular cases have been recently studied. In [2], for instance, the dominating number of the zero divisor graph of the ring of Gaussian integers modulo n was studied. In particular, the authors characterized the values of n for which the domination number of Γ(Z n [i]) is 1 or 2.…”

“…Lemma 11. The intersection of a right annihilator of type (2) or (3) with a left annihilator of type (4) or (5) is a set with p elements.…”

“…, D k }, where k < p + 1. Hence, there is a right annihilator ann r (X) of type (2) or (3) that is not among the k right annihilators ann r (D 1 ), . .…”

“…The zero divisor graph of the ring of Gaussian integers modulo n has recently received great attention [1,2,22].…”

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

“…Γ R for rings R which satisfy certain conditions are discussed by Anderson and Badawi 5 . The zero divisor graph of the ring of integers modulo n was extensively studied in 6-10 . In 2008, Abu Osba et al 11 introduced the zero divisor graphs for the ring of Gaussian integers modulo n, Γ Z n i , where they studied several graph properties and 2 International Journal of Combinatorics determined several graph invariants for Γ Z n i . Further properties of the zero divisor graphs for the ring of Gaussian integers modulo n are investigated in 12 . In this paper, we study the line graph of Γ Z n i .…”