Union of subgraphs with respect to some ideals on near rings

Al-alawani, Awrad A.; Al-Swidi, Ameer A. J.

doi:10.47974/JDMSC-2048

Open Access Research Article

Union of subgraphs with respect to some ideals on near rings

^*Awrad A. Al-alawaniCorresponding authorawrad.alalwani@gmail.comDepartment of MathematicsCollege of Education for Pure ScienceUniversity of BabylonBabylon, 51002, IraqView full profile → , Ameer A. J. Al-Swidiameer.alswidi@yahoo.comDepartment of MathematicsCollege of Education for Pure ScienceUniversity of BabylonBabylon, 51002, Iraq0000-0002-8560-2072View full profile →

* Corresponding author · click or hover a name for details

pp. 399–408Vol. 28Issue 2March 2025DOI: 10.47974/JDMSC-2048 Crossmark XML

Received:: 08 May 2024
Published Online:: 21 Mar 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2048
Pages:: 399–408

Abstract

In our work, the new concept of union in certain graphs: WI(N), API(N), ΓI(N) and PGI(N) are dealt, which depends on the case of the intersection of edges in the subgraphs in which it equals an empty set, as well as a study of the case of homomorphism, where we reached many new theorems and Results that can be generalized to other graphs or algebra graph theory.

Keywords

Joining edge Completely prime ideal Weakly completely prime ideal Epimorphism Indempotent ideal Almost 1-prime ideal Almost 2-prime ideal Almost 3-prime ideal

Subject Classifications

05C92

References

[1] G. Pilz, Near-rings: The Theory and Its Applications, North Holland (1983). doi: 10.1016/C2013-0-03739-6.
[2] N. Deo, Graph Theory with Applications to Engineering and Computer Science, Courier Dover Publications (2017).
[3] A. A. AL-Swidi and A. Omran, “Weakly completely prime graph,” Wasit Journal for Pure Sciences, vol. 2, no. 1, pp. 156-163 (2023).
[4] A. A. AL-alawani, A. A. AL-Swidi, “New types of ideals on near rings,” in AIP Conference Proceedings, accepted for publication (2024).
[5] I. Beck, “Coloring of commutative rings,” Journal of Algebra, vol. 116, no. 1, pp. 208-226 (1988). doi: 10.1016/0021-8693(88)90202-5.
[6] S. Bhavanari, S. Kuncham, and N. Dasari, “Prime graph of a ring,” Journal of Combinatorics, Information and System Sciences, vol. 35, no. 1-2, pp. 1-2 (2010).
[7] S. M. Kadham and A. N. Alkiffai, “Generalization of Fuzzy SHA-Transform with Medical Application,” Mathematical Modelling of Engineering Problems, vol. 9, no. 5 (2022).
[8] A. A. AL-Swidi and A. Omran, “Completely equiprime graph of a near ring,” in AIP Conference Proceedings (2021).
[9] A. A. AL-Swidi and A. Omran, “Uniquely colorable completely equiprime graph of a near ring,” in AIP Conference Proceedings (2021).
[10] A. A. AL-Swidi, E. H. AL-Saadi, and L. H. AL-Saadi, “Soft public key cipher,” Periodicals of Engineering and Natural Sciences, vol. 7, no. 3, pp. 1433-1438 (2019).
[11] M. A. Mustafa, S. M. Kadham, N. K. Abbass, S. Karupusamy, H. Y. Jasim, B. A. Alreda, et al., “A novel fuzzy M-transform technique for sustainable ground water level prediction,” Applied Geomatics, vol. 16, no. 1, pp. 9-15 (2024).
[12] A. A. AL-Swidi and A. A. Omran, “Study of some graph types via soft graph,” ARPN Journal of Engineering, vol. 14, no. 8, pp. 10375-10379 (2019).
[13] W. V. Kandasamy, Smarandache Near-Rings, Infinite Study (2002).
[14] A. Sundud Najah Jabir, S. Maki Kadham, M. A. Ahmed Mustafa, and N. K. Abbass, “Encryption and enhance medical image using hybrid transform (â-module and partial fuzzy Ĥ-transform),” Journal of Discrete Mathematical Sciences and Cryptography, vol. 26, no. 7, pp. 1903–1910 (2023). doi: 10.47974/JDMSC-1683.
[15] H. E. Bell, “Near-rings in which each element is a power of itself,” Bulletin of the Australian Mathematical Society, vol. 2, no. 3, pp. 363-368 (1970). doi: 10.1017/S0004972700041563.
[16] J. L. Gross, J. Yellen, and M. Anderson, Graph Theory and Its Applications, 3rd ed., Chapman and Hall/CRC (2018). doi: 10.1201/9780429425134.
[17] J. L. Gross, J. Yellen, and M. Anderson, Graph Theory and Its Applications, ACM Digital Library (2018). doi: 10.1145/3274895.
[18] J. Huo, S. Wen, Y. Chen, and M. Li, “Neighbor distinguishing colorings of graphs with the restriction for maximum average degree,” Axioms, vol. 12, no. 12, p. 1132 (2023). doi: 10.3390/axioms12121132.
[19] W. Gao and M. R. Farahani, “The hyper-Zagreb index for an infinite family of nanostar dendrimer,” J. Discrete Math. Sci. Cryptography, vol. 20, no. 2, pp. 515-523 (2017). doi: 10.1080/09720529.2016.1220088.
[20] W. Gao, L. Shi, and M. R. Farahani, “Szeged related indices of TUAC6[p, q],” J. Discrete Math. Sci. Cryptography vol. 20, no. 2, pp. 553-563 (2017). doi: 10.1080/09720529.2016.1228312.
[21] H. Yang and X. Zhang, “The independent domination numbers of strong product of two cycles,” J. Discrete Math. Sci. Cryptography, vol. 21, no. 7-8, pp. 1495-1507 (2018). doi: 10.1080/09720529.2017.1316988.
[22] S. Ediz, İ. Çiftçi, M. Cancan, and M. R. Farahani, “On k-total distance degrees and k-total Wiener polarity index,” J. Inform. Optim. Sci., vol. 42, no. 7, pp. 1469-1477 (2021). doi: 10.1080/02522667.2021.1896652.
[23] F. Afzal, Shah Rukh, D. Afzal, M. R. Farahani, M. Cancan, and S. Ediz, “A study of non-commutative Von-Neumann regular rings,” J. Inform. Optim. Sci., vol. 42, no. 7, pp. 1425-1436 (2021). doi: 10.1080/02522667.2021.1896650.
[24] M. S. Sardar, M. Alaeiyan, M. R. Farahani, M. Cancan, and S. Ediz, “Resistance distance in some classes of rooted product graphs obtained by Laplacian generalized inverse method,” J. Inform. Optim. Sci., vol. 42, no. 7, pp. 1447-1467 (2021). doi: 10.1080/02522667.2021.1899210.
[25] M. Nadeem, S. Ahmad, M. K. Siddiqui, M. A. Ali, M. R. Farahani, and A. J. M. Khalaf, “On some applications related with algebraic structures through different well known graphs,” J. Discrete Math. Sci. Cryptography, vol. 42, no. 2, pp. 451-471 (2021). doi: 10.1080/09720529.2021.1885806.
[26] M. R. Farahani, S. Jafari, S. A. Mohiuddine, and M. Cancan, “Intuitionistic fuzzy stability of generalized additive set-valued functional equation via fixed point method,” Mathematical Statistician and Engineering Applications, vol. 71, no. 3s3, pp. 142-154 (2022). [Online]. Available: https://www.philstat.org.ph/index.php/MSEA/article/view/355.
[27] R. F. Kadam and K. M. Mohammed Al-Abrahemee, “Neuro-fuzzy system for solving fuzzy singular perturbation problems,” J. Interdiscip. Math., vol. 25, no. 5, pp. 1509-1524 (2022). doi: 10.1080/09720502.2022.2079229.
[28] D. E. Abdulrasool and A. N. Alkiffai, “Population growth equation by fuzzy common integral transforms,” J. Interdiscip. Math., vol. 25, no. 6, pp. 1909-1918 (2022). doi: 10.1080/09720502.2022.2095960.
[29] A. H. Alwan, “Small intersection graph of subsemimodules of a semimodule,” Commun. Combin. Cryptogr. Comput. Sci., vol. 2022, no. 1, pp. 15-22 (2022).
[30] S. Ediz, M. Cancan, and M. R. Farahani, “Eccentric connectivity and connective eccentricity indices of generalized Petersen graphs,” Commun. Combin. Cryptogr. Comput. Sci., vol. 2021, no. 1, pp. 1-6 (2021).
[31] R. Ponraj, S. Prabhu, and M. Sivakumar, “Pair mean cordial labeling of total graph of some graphs and prism related graphs,” Commun. Combin. Cryptogr. Comput. Sci., vol. 2024, no. 2, pp. 181-192 (2024).
[32] F. O. Oduol and I. O. Okoth, “Counting vertices among all noncrossing trees by levels and degrees,” Commun. Combin. Cryptogr. Comput. Sci., vol. 2024, no. 2, pp. 193-212 (2024).

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