542a369f-3f60-4890-8ac1-d55190977a3f20210223122441908wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS2224-28801109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40512720202720201910.37394/23206.2020.19http://wseas.org/wseas/cms.action?id=23185Planar of Special Idealization RingsManalAl-LabadiEman Mohammad Almuhur, Department of Mathematics, University of Petra, Amman, JORDAN, also with Department of Mathematics,Faculty of Basic Sciences and Humanities,Applied Science Private University,Amman, JordanLet R(+)N be the idealization of the ring R by the R-module N. In this paper, we investigate when Γ(R(+)N) is a Planar graph where R is an integral domain and we investigate when Γ(Zn(+)Zm) is a Planar graph.1223202012232020606609https://www.wseas.org/multimedia/journals/mathematics/2020/b345106-041.pdf10.37394/23206.2020.19.66https://www.wseas.org/multimedia/journals/mathematics/2020/b345106-041.pdfM. Allabadi M., Futher results on the diameter of zero-divisor graphs of some special idealizations,International Journal of Algebra, Vol. 12 (2010), pp. 609-614.M. Allabadi, On the Diameter of Zero-Divisor Graphs of Idealizations with Respect to Integral Domain,Jordan Journal of Mathematics and Statistics, Vol. 3 (2010), pp. 127-131.10.1006/jabr.1993.1171D. D. Anderson, M. Naseer, Beck’s coloring of a commutative ring, J. Algebra, Vol.159 (1993), pp. 500-514.10.1006/jabr.1998.7840D. F. Anderson, P. S. Livingston, The zero-divisor graph of a commutative, J. Algebra, Vol. 217 (1999), pp. 434-447.M. Axtell, J. Stickle, The zero-divisor graph of a commutative rings, textit Journal of Pure and Applied Algebra, Vol.204 (2006), pp. 235-243.I. Beck, Coloring of a commutative ring, J. Algebra, Vol. 116 (1988), pp. 208-226.B. Jackson, Longest cycles in 3-connectedcubic, J. Combin. Theory Ser B, Vol. 41 (1986), pp. 17-26.N. Boonsim, Racing Bib Number Localization on Complex Backgrounds, WSEAS Transactions on Systems and Control, Vol.13 (2018), pp. 226-231.T. Ashkan Tashk, H. Jurgen, Esmaeil Nadimi, Automatic Segmentation of Colorectal Polyps based on a Novel and Innovative Convolutional Neural Network Approach, WSEAS Transactions on Systems and Control, Vol.14 (2019), pp. 384-391.