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Zbl 1151.05042
Osba, Emad Abu; Al-Addasi, Salah; Jaradeh, Nafiz Abu
Zero divisor graph for the ring of Gaussian integers modulo $n$. (English)
[J] Commun. Algebra 36, No. 10, 3865-3877 (2008). ISSN 0092-7872; ISSN 1532-4125/e

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

MSC 2000:: *05C75 Structural characterization of types of graphs
13A99 General commutative ring theory

Keywords: bipartite graph; complete graph; diameter; Eulerian graph; Gaussian integers; girth; graph; planar graph; zero divisor graph

Cited in: Zbl 1213.13019

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