On the Line Graph of the Zero Divisor Graph for the Ring of Gaussian Integers Modulo n. (29th January 2012)

• Record Type: Journal Article
• Authors: Nazzal Nazzal, Khalida Khalida; Ghanem Ghanem, Manal Manal
• Other Names: Salazar Salazar Gelasio Gelasio Academic Editor.
• Is Part Of: International journal of combinatorics. Volume 2012(2012)
• Publication Date: 2012-01-29
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Periodicals; Electronic journals; 511.605
• DOI: 10.1155/2012/957284
• Languages: English
• ISSNs: 1687-9163

Abstract

Abstract : Let Γ ( ℤ n [ i ]) be the zero divisor graph for the ring of the Gaussian integers modulo n . Several properties of the line graph of Γ ( ℤ n [ i ]), L(Γ ( ℤ n [ i ])) are studied. It is determined when L(Γ ( ℤ n [ 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 ( ℤ n [ i ])) is given when n is a power of a prime. On the other hand, several graph invariants for Γ ( ℤ n [ i ]) are also determined.