Author(s)

Manal Ghanem, Khalida Nazzal

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The line graph for the complement of the zero divisor graph for the ring of Gaussian integers modulo n is studied. The diameter, the radius and degree of each vertex are determined. Complete characterization of Hamiltonian, Eulerian, planer, regular, locally and locally connected is given. The chromatic number when is a power of a prime is computed. Further properties for and are also discussed.

Complement of a Graph; Chromatic Index; Diameter; Domination Number; Eulerian Graph; Gaussian Integers Modulo n; Hamiltonian Graph; Line Graph; Radius; Zero Divisor Graph

M. Ghanem and K. Nazzal, "On the Line Graph of the Complement Graph for the Ring of Gaussian Integers Modulo n," Open Journal of Discrete Mathematics, Vol. 2 No. 1, 2012, pp. 24-34. doi: 10.4236/ojdm.2012.21006.