Zero Divisor Graph for the Ring of Gaussian Integers Modulo n |
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| Authors: | Emad Abu Osba Salah Al-Addasi Nafiz Abu Jaradeh |
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| Institution: | 1. Mathematics Department, Faculty of Science , University of Jordan , Amman, Jordan eabuosba@ju.edu.jo;3. Mathematics Department, Faculty of Science , Hashemite University , Zarqa, Jordan;4. Mathematics Department, Faculty of Science , University of Jordan , Amman, Jordan |
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| Abstract: | This article studies the zero divisor graph for the ring of Gaussian integers modulo n, Γ (? n i]). For each positive integer n, the number of vertices, the diameter, the girth and the case when the dominating number is 1 or 2 is found. Complete characterizations, in terms of n, are given of the cases in which Γ (? n i]) is complete, complete bipartite, planar, regular or Eulerian. |
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| Keywords: | Bipartite graph Complete graph Diameter Eulerian graph Gaussian integers Girth Graph Planar graph Zero divisor graph |
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