The Zero Divisor Graph of the Ring Z_(2^2 p)

Nazar H. Shuker; Payman A. Rashed

doi:10.14500/aro.10058

The Zero Divisor Graph of the Ring Z_(2^2 p)

Nazar H. Shuker Department of Mathematic, College of Computer Sciences and Mathematic, University of Mosul, Mosul
Payman A. Rashed Department of Mathematic, College of Basic Education, University of Salahaddin, Erbil, Kurdistan Region

DOI: https://doi.org/10.14500/aro.10058

Keywords: Bipartite graph, crossing number, girth, planar graph, zero divisor graph of the ring Z_(2^2 p).

Abstract

In this paper, we consider the crossing number and the chromatic number of the zero divisor graph Γ(Z_(2^2 p)) to show that this type of zero divisor graphs is bipartite graph, and the smallest cycle in Γ(Z_(2^2 p)) is of length four this implies that the girth is equal four.

Downloads

Download data is not yet available.

References

Anderson, D.D. and Livingston, P.S., 1999. The zero divisor graph of a commutative ring. Journal of Algebra, 217, pp.434-447.

Beck, I., 1988. Coloring of commutative ring. Journal of Algebra, 116, pp208-226.

Bondy, J.A. and. Murty, U.S.R., 2013. Graph Theory and Application North. Holland, New York. Amsterdam. Oxford.

Coykendall, J., Wagstaff, S.S., Sheppardon, L. and Spiroff, S., 2012. On zero divisor graph. Journal of Commutative Algebra, 2, pp.241-299.

Duane, A., 2006. Proper coloring and p-partite structures of the zero divisor graph. Rose Holman Undergraduate Math Journal, 7(2), pp.1-7.

Harary, F., 1969. Graph Theory. Addison-Wesley Publishing Company, California.

Harju, T., 2005. Graph theory, Department of Mathematics, University of Turku, Finland.

Malathi, M., Sankeetha, S. and Sankar, J.R., 2013. Rectilinear crossing number of a zero divisor graph. International Mathematical Forum, 8(12), pp583-589.

Sankar, J.R. and Sankeetha, S., 2012. Crossing number of a zero divisor graph. International Journal of Algebra, 6(32), pp.1499-1505.

Shuker, N.H., Mohammad, H.Q. and Ali, A.M., 2012. The zero divisor graph of Z_(p^n q) . International Journal of Algebra, 6, pp.1049-1055.

View The PDF File

Published

2016-12-23

How to Cite

Shuker, N. H. and Rashed, P. A. (2016) “The Zero Divisor Graph of the Ring Z_(2^2 p)”, ARO-THE SCIENTIFIC JOURNAL OF KOYA UNIVERSITY, 4(2), pp. 47-50. doi: 10.14500/aro.10058.

Download Citation

Issue

Vol. 4 No. 2 (2016): Issue Seven

Section

Articles

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Authors who choose to publish their work with Aro agree to the following terms:

Authors retain the copyright to their work and grant the journal the right of first publication. The work is simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-SA 4.0]. This license allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Authors have the freedom to enter into separate agreements for the non-exclusive distribution of the journal's published version of the work. This includes options such as posting it to an institutional repository or publishing it in a book, as long as proper acknowledgement is given to its initial publication in this journal.
Authors are encouraged to share and post their work online, including in institutional repositories or on their personal websites, both prior to and during the submission process. This practice can lead to productive exchanges and increase the visibility and citation of the published work.

By agreeing to these terms, authors acknowledge the importance of open access and the benefits it brings to the scholarly community.