Zero divisor graph for the ring of Gaussian integers modulo \(n\). (English) Zbl 1151.05042

Summary: This article studies the zero divisor graph for the ring of Gaussian integers modulo \(n, \Gamma (\mathbb Z_n[i])\). 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 \(\Gamma (\mathbb Z_n[i])\) is complete, complete bipartite, planar, regular or Eulerian.


05C75 Structural characterization of families of graphs
13A99 General commutative ring theory
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