Osba, Emad Abu; Al-Addasi, Salah; Jaradeh, Nafiz Abu Zero divisor graph for the ring of Gaussian integers modulo \(n\). (English) Zbl 1151.05042 Commun. Algebra 36, No. 10, 3865-3877 (2008). 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. Cited in 2 ReviewsCited in 7 Documents MSC: 05C75 Structural characterization of families of graphs 13A99 General commutative ring theory Keywords:bipartite graph; complete graph; diameter; Eulerian graph; Gaussian integers; girth; graph; planar graph; zero divisor graph PDF BibTeX XML Cite \textit{E. A. Osba} et al., Commun. Algebra 36, No. 10, 3865--3877 (2008; Zbl 1151.05042) Full Text: DOI OpenURL References: [1] Abu Osba E. A., Comment. Math. Univ. Carolinea 47 (1) pp 1– (2006) [2] Akbari S., J. Algebra 270 pp 169– (2003) · Zbl 1032.13014 [3] Anderson D. F., J. Algebra 217 pp 434– (1999) · Zbl 0941.05062 [4] Axtell M., Houston J. Math. 32 (4) pp 985– (2006) [5] Cross J., Amer. Math. Monthly 90 (8) pp 518– (1983) · Zbl 0525.12001 [6] Mulay S. B., Comm. Algebra 30 (7) pp 3533– (2002) · Zbl 1087.13500 [7] Silverman J., A Friendly Introduction to Number Theory., 3. ed. (2006) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.