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On the Line Graph of the Complement Graph for the Ring of Gaussian Integers Modulo n
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Open Journal of Discrete Mathematics·Volume 02 (2012)·Pages 24–34·Published 20 January 2012·DOI10.4236/ojdm.2012.21006
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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.
KeywordsComplement of a GraphChromatic IndexDiameterDomination NumberEulerian GraphGaussian Integers Modulo nHamiltonian GraphLine GraphRadiusZero Divisor Graph
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