Osba, Emad Abu; Al-Addasi, Salah; Al-Khamaiseh, Basem Some properties of the zero-divisor graph for the ring of Gaussian integers modulo \(n\). (English) Zbl 1213.13019 Glasg. Math. J. 53, No. 2, 391-399 (2011). Summary: This paper is a continuation for the study of the zero-divisor graph for the ring of Gaussian integers modulo \(n\), \(\Gamma (\mathbb Z_{n}[i])\) in [E. A. Osba, S. Al-Addasi and N. A. Jaradeh, Commun. Algebra 36, No. 10, 3865–3877 (2008; Zbl 1151.05042)]. It is investigated, when is \(\Gamma (\mathbb Z_{n}[i])\) locally \(H\), Hamiltonian or bipartite graph? A full characterisation for the chromatic number and the radius is also given. Cited in 4 Documents MSC: 13A99 General commutative ring theory 05C15 Coloring of graphs and hypergraphs Citations:Zbl 1151.05042 PDF BibTeX XML Cite \textit{E. A. Osba} et al., Glasg. Math. J. 53, No. 2, 391--399 (2011; Zbl 1213.13019) Full Text: DOI OpenURL References: [1] Osba, Comment. Math. Univ. Carolinea 47 pp 1– (2006) [2] DOI: 10.1080/00927870802160859 · Zbl 1151.05042 [3] Duane, Rose Hulman Undergrad. Math. J. 7 pp 1– (2006) [4] Doob, Handbook of Graph Theory pp 557– (2004) [5] Wilson, Introduction to graph theory (1996) · Zbl 0891.05001 [6] Chiang-Hsieh, Houst. J. Math. 36 pp 1– (2010) [7] Cameron, Topics in algebraic graph theory pp 137– (2005) [8] Buckly, A friendly introduction to graph theory (2003) [9] DOI: 10.1006/jabr.1998.7840 · Zbl 0941.05062 [10] DOI: 10.2307/30037545 · Zbl 1138.11344 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.