## 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.

### MSC:

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

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