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SOME PROPERTIES OF THE ZERO-DIVISOR GRAPH FOR THE RING OF GAUSSIAN INTEGERS MODULO n

Published online by Cambridge University Press:  21 March 2011

EMAD ABU OSBA ,
SALAH AL-ADDASI  and
BASEM AL-KHAMAISEH
EMAD ABU OSBA
Affiliation:
Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan e-mail: eabuosba@ju.edu.jo
SALAH AL-ADDASI
Affiliation:
Department of Mathematics, Faculty of Science, Hashemite University, Zarqa 13115, Jordan e-mail: salah@hu.edu.jo
BASEM AL-KHAMAISEH
Affiliation:
Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan e-mail: basem198426@yahoo.com
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Abstract

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This paper is a continuation for the study of the zero-divisor graph for the ring of Gaussian integers modulo n, Γ(ℤn[i]) in [8] (Emad Abu Osba, Salah Al-Addasi and Nafez Abu Jaradeh. Zero divisor graph for the ring of Gaussin integers modulo n. Comm. Algebra 36(10) (2008), 3865–3877). It is investigated, when is Γ(ℤn[i]) locally H, Hamiltonian or bipartite graph? A full characterisation for the chromatic number and the radius is also given.

Keywords

13A9905C15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 2 , May 2011 , pp. 391 - 399
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

REFERENCES

1.Anderson, D. F. and Livingston, P. S., The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), 434–447.CrossRefGoogle Scholar
2.Buckly, F. and Lewinter, M., A friendly introduction to graph theory (Person Prentice Hall, New Jersy, 2003).Google Scholar
3.Cameron, P. J., Automorphisms of graphs, in: Topics in algebraic graph theory (Beineke, L. W. and Wilson, R. J., Editors) (Cambridge University Press, Cambridge, UK, 2005), 137–155.Google Scholar
4.Chiang-Hsieh, H-J. and Wang, H-J., Commutative rings with toroidal zero-divisor graphs, Houst. J. Math. 36 (1) (2010), 1–31.Google Scholar
5.Dersden, G. and Dymàček, W. M., Finding factors of factor rings over the Gaussian integers, Amer. Math. Monthly 112 (7) (2005), 602–611.CrossRefGoogle Scholar
6.Doob, M., Spectral graph theory, in: Handbook of Graph Theory (Gross, J. L. and Yellen, J., Editors) (CRC Press LLC, Boca Raton, 2004), 557–573.Google Scholar
7.Duane, A., Proper colorings and p-partite structures of the zero divisor graph, Rose Hulman Undergrad. Math. J. 7 (2) (2006), 1–7.Google Scholar
8.Osba, E. A., Al-Addasi, S. and Jaradeh, N. A., Zero divisor graph for the ring of Gaussin integers modulo n. Comm. Algebra 36 (10) (2008), 3865–3877.CrossRefGoogle Scholar
9.Osba, E. A., Henriksen, M., Alkam, O. and Smith, F., The maximal regular ideal of some commutative rings. Comment. Math. Univ. Carolinea 47 (1) (2006), 1–10.Google Scholar
10.Wilson, R., Introduction to graph theory, 4th edn. (Pearson Prentice Hall, Malaysia, 1996).Google Scholar