International Journal of Nonlinear Analysis and Applications
New type graph with respect to ideal near ring
Document Type : Research Paper
Authors
Department of Mathematics, College of Education for Pure Science, University of Babylon, Iraq
Abstract
A weakly completely prime graph of a near ring $(W_I (N))$ was defined in this paper, the relationship between the elements of a near ring was determined by a definition of weakly completely prime ideal, so we studied many concepts related to the statements of the given near ring. We also found some theories related to previous graphs of our papers.
Keywords
[1] M.A. Abbood, A.A.J. AL-Swidi and A.A. Omran, Study of some graphs types via. soft graph, J. Eng. Appl. Sci.
14 (2019), 10375–10379.
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no. 3, 1433–1438.
[3] A.A.J. Al-swidi, E.H. Al-Saadi and R.A.A. Shekan, Huffman code via fuzzy generators, J. Eng. Appl. Sci. 13
(2018), no. 22, 9735–9738.
[4] A.A.J. Al-swidi and A.A. Omran, Completely equiprime graph of a near ring, 1st Int. Conf. Pure Sci. 2021.
[5] A.A.J. Al-swidi and A.A. Omran, Uniquely colorable completely equiprime graph of a near ring, 2nd Int. Conf.
Pure Sci. 2021.
[6] D.D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math. 4 (2003), 831—840.
[7] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), 208–226.
[8] H.E. Bell, Near-rings in which each element is a power of itself, Bull. Aust. Math. Soc. 2 (1970), no. 3, 363–368.
[9] S. Bhavanari, S. Kuncham and N. Dasari, Prime graph of a ring, J. Combinatorics, Info. Syst. Sci. 35 (2010),
1–2.
[10] N. Deo, Graph theory with applications to engineering and computer science, Courier Dover Publications, 2017.
[11] N.J. Groenwald, The completely prime radical in near-rings, Acta Math. Hungar. 51 (1988), 301–305.
[12] A.A. Jabor and A.A. Omran, Hausdorff topological of path in graph, IOP conf. Ser.: Materials Sci. Eng. 928
(2020), no. 4, 042008.
[13] A.A. Jabor and A.A. Omran, Topological domination in graph theory, AIP Conf. Proc. 2334 (2021), no. 1, 020010.
[14] W.B.V. Kandasamy, Smarandache near-rings, Infinite Study, 2002.
[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, 726–734.
[16] G. Pilz, Near-rings: the theory and its applications, North Hollond, 1983.
[17] S.H. Talib, A.A. Omran and Y. Rajihy, Additional properties of frame domination in graphs, J. Phys.: Conf. Ser.
1664 (2020), no. 1, 012026.
[18] C. Vasudev, Graph theory with applications, New Age International, 2006.
[19] G. Wendt, On zero divisors in near-rings, Int. J. Algebra 3 (2009), no. 1, 21–32.
14 (2019), 10375–10379.
[2] A.A.J. Al-swidi, E.H. Al-Saadi and L.H. Al-Saad, Soft public key cipher, Period. Engin. Natural Sci. 7 (2019),
no. 3, 1433–1438.
[3] A.A.J. Al-swidi, E.H. Al-Saadi and R.A.A. Shekan, Huffman code via fuzzy generators, J. Eng. Appl. Sci. 13
(2018), no. 22, 9735–9738.
[4] A.A.J. Al-swidi and A.A. Omran, Completely equiprime graph of a near ring, 1st Int. Conf. Pure Sci. 2021.
[5] A.A.J. Al-swidi and A.A. Omran, Uniquely colorable completely equiprime graph of a near ring, 2nd Int. Conf.
Pure Sci. 2021.
[6] D.D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math. 4 (2003), 831—840.
[7] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), 208–226.
[8] H.E. Bell, Near-rings in which each element is a power of itself, Bull. Aust. Math. Soc. 2 (1970), no. 3, 363–368.
[9] S. Bhavanari, S. Kuncham and N. Dasari, Prime graph of a ring, J. Combinatorics, Info. Syst. Sci. 35 (2010),
1–2.
[10] N. Deo, Graph theory with applications to engineering and computer science, Courier Dover Publications, 2017.
[11] N.J. Groenwald, The completely prime radical in near-rings, Acta Math. Hungar. 51 (1988), 301–305.
[12] A.A. Jabor and A.A. Omran, Hausdorff topological of path in graph, IOP conf. Ser.: Materials Sci. Eng. 928
(2020), no. 4, 042008.
[13] A.A. Jabor and A.A. Omran, Topological domination in graph theory, AIP Conf. Proc. 2334 (2021), no. 1, 020010.
[14] W.B.V. Kandasamy, Smarandache near-rings, Infinite Study, 2002.
[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, 726–734.
[16] G. Pilz, Near-rings: the theory and its applications, North Hollond, 1983.
[17] S.H. Talib, A.A. Omran and Y. Rajihy, Additional properties of frame domination in graphs, J. Phys.: Conf. Ser.
1664 (2020), no. 1, 012026.
[18] C. Vasudev, Graph theory with applications, New Age International, 2006.
[19] G. Wendt, On zero divisors in near-rings, Int. J. Algebra 3 (2009), no. 1, 21–32.
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Volume 13, Issue 2
July 2022Pages 1297-1304
- Receive Date: 09 November 2021
- Revise Date: 22 December 2021
- Accept Date: 11 February 2022