On the Line Graph of the Complement Graph for the Ring of Gaussian Integers Modulo n

Manal Ghanem, Khalida Nazzal

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DOI: 10.4236/ojdm.2012.21006                

Abstract

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

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