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OALib Journal期刊
ISSN: 2333-9721
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On the Line Graph of the Zero Divisor Graph for the Ring of Gaussian Integers Modulo

DOI: 10.1155/2012/957284

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Abstract:

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

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