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The radius, diameter and chromatic number of some zero divisor graph | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3891-3896 اصل مقاله (1.08 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6189 | ||
| نویسندگان | ||
| Hayder F. Ghazi* ؛ Ahmed Omran | ||
| Department of Mathematics, College of Education for Pure Science, University of Babylon, Babylon, Iraq | ||
| تاریخ دریافت: 16 تیر 1400، تاریخ بازنگری: 28 مرداد 1400، تاریخ پذیرش: 12 مهر 1400 | ||
| چکیده | ||
| In this work, the radius, diameter and a chromatic number of zero divisor graph of the ring $Z_n$ for some n are been determined. These graphs are ${\Gamma }\left(Z_{p^2q^2}\right)$, ${\Gamma }\left(Z_{p^2}\right)$, ${\Gamma}\left(Z_{pq}\right)$, ${\Gamma }\left(Z_{p^3}\right)$, ${\Gamma }\left(Z_{p^2q}\right)$ and ${\Gamma }\left(Z_{pqr}\right)$. Furthermore, the largest induced subgraph isomorphic to complete subgraph in the graph ${\Gamma }\left(Z_{p^3}\right)$ and $\mathit{\Gamma}(p^2q)$ are calculated. | ||
| کلیدواژهها | ||
| Zero divisor graph؛ Radius؛ Diameter؛ Chromatic number | ||
| مراجع | ||
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[1] M.A. Abbood, A.A. AL-Swidi and A.A. Omran, Study of some graphs types via soft graph, ARPN J. Eng. Appl. Sci. 14 (Special Issue 8) (2019) 10375–10379. [2] K.S. Al’Dzhabri, A.A. Omran and M.N. Al-Harere, DG-domination topology in Digraph, J. Prime Res. Math. 17(2) (2021) 93–100. [3] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988) 208–226. [4] C. Berge, The Theory of Graphs and its Applications, Methuen and Co., London, 1962. [5] G. Chartrand and L. Lesniak, Graphs and Digraphs, Chapman & Hall/CRC, 2005. [6] F. Harary, Graph Theory, Addison-Wesley, Reading, Mass., 1969. [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, NY, USA, 1998. [8] F. Harary, Graph Theory, Addison-Wesley Reading MA, USA, 1969. [9] H.F. Ghazi, A.A. Omran, Domination of some zero divisor graph and its complement, Third Int. Sci. Conf. ICCEPS, 2021. [10] A.A. Omran and H.F. Ghazi, Some properties of zero divisor graph in the ring Zn for some n, AIP Conf. Proc. 2019. [11] T.A. Ibrahim and A.A. Omran, Restrained whole domination in graphs, J. Phys. Conf. Ser. 1879 (2021) 032029. [12] A.A. Jabor and A.A. Omran, Topological domination in graph theory, AIP Conf. Proc. 2334(1) (2021) 020010. [13] S.S. Kahat, A.A. Omran and M.N. Al-Harere, Fuzzy equality co-neighborhood domination of graphs, Int. J. Nonlinear Anal. Appl. 12(2) (2021) 537–545. [14] A.A. Omran and M.M. Shalaan, Inverse Co-even Domination of Graphs, IOP Conf. Ser. Mater. Sci. Eng. 928 (2020) 042025. [15] A. A. Omran and T. A. Ibrahim, Fuzzy co-even domination of strong fuzzy graphs, Int. J. Nonlinear Anal. Appl. 12(2021) No. 1, 727-734. [16] M.M. Shalaan and A.A. Omran, Co-even domination number in some graphs, IOP Conf. Ser. Mater. Sci. Eng. 928 (2020) 042015. [17] Y. Rajihy, Some properties of total frame domination in graphs, J. Eng. Appl. Sci. 13(Special issue1) (2018). [18] S.H. Talib, A.A. Omran and Y. Rajihy, Additional properties of frame domination in graphs, J. Phys. Conf. Ser. 1664(1) (2020). [19] S.H. Talib, A.A. Omran and Y. Rajihy, Inverse frame domination in graphs, IOP Conf. Ser. Mater. Sci. Engin. 928(4) (2020). [20] H.J. Yousif and A.A. Omran, Closed fuzzy dominating set in fuzzy graphs, J. Phys. Conf. Ser. 1879 (2021) 032022. [21] H.J. Yousif and A.A. Omran, Some results on the n-fuzzy domination in fuzzy graphs, J. Phys. Conf. Ser. 1879 (2021) 032009. [22] H.J. Yousif and A.A. Omran, Inverse 2- anti fuzzy domination in anti fuzzy graphs, J. Phys. Conf. Ser. 1818 (2021) 012072. | ||
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