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Open Access Research Article

Co-regular captive domination number γcrg in graphs

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pp. 569–575Vol. 28Issue 2March 2025DOI: 10.47974/JDMSC-2259 Crossmark XML
Received:
06 Nov 2024
Published Online:
11 Apr 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2259
Pages:
569–575

Abstract

This paper initiated the new domination number, which is named the co-regular captive, it is linked to two numbers of dominations they are captive domination number (CDN) and r-regular captive domination number. Many of the bounded, properties, and theorems of this domination are determined.

Keywords

Subject Classifications

68Rxx68-XX68Uxx

References

[1] M. N. Al-Harere, A.A. Omran, and A. T. Breesam, “Captive domination in graphs,” Discrete Math. Algorithms Appl., vol. 12, no. 06, pp. 2050076-2050076 (2020). [Online] Available: https://doi.org/10.1142/s1793830920500767.
[2] C. Berge, The theory of graphs and its applications, Methuen and Co, London (1962). 
[3] F. Harary, Graph theory, Addison-Wesley, Reading, Mass. (1969).
[4] T.A. Ibrahim and A.A. Omran, Restrained Whole Domination in Graphs, J. Phys.: Conf. Ser. 1879, pp. 032029 (2021). [Online] Available: https://doi.org/10.1088/1742-6596/1879/3/032029. 
[5] A. A. Omran and T. A. Ibrahim, “Fuzzy co-even domination of strong fuzzy graphs,” Int. J. Nonlinear Anal. Appl., vol. 12, no. 1, pp. 726-734 (2021). [Online] Available: https://doi.org/10.22075/ijnaa.2021.4934.
[6] S. S. Kahat, A.A. Omran, and M.N. Al-Harere, Fuzzy equality co-neighborhood domination of graphs, Int. J. Nonlinear Anal. Appl., vol. 12, No. 2, pp. 537-545 (2021). [Online] Available: https://doi.org/10.22075/ijnaa.2021.5101.
[7] Z. Y. Alrikabi, A.A. Omran, and H.J. Al-Hawaeer, The captive domination number of graphs constructed by deleting a vertex (an edge) and addition or contraction of an edge,” AIP conference proceedings, vol. 3224, pp. 070022-070022 (2025). [Online] Available: https://doi.org/10.1063/5.0254094.
[8] Z.Y. Alrikabi and A.A. Omran, Examining Captive and Inverse Captive Domination in Selected Graphs and Their Complements, Math. Model. Eng. Probl., vol. 10, no. 5, pp. 1763-1769 (2023). [Online] Available: https://doi.org/10.18280/mmep.100527. 
[9] Z.Y. Alrikabi, A.A. Omran, and H.J. Al-Hwaeer, “Restrained captive domination number,” Open Engineering, vol. 14, no. 1 (2024). [Online] Available: https://doi.org/10.1515/eng-2022-0510.
[10] Z. Y. Alrikabi, A.A. Omran, and H.J. Al-Hwaeer, “Double captive domination number (DCDN),” J. Discrete Math. Sci. Cryptogr., vol. 27, no. 5, pp. 1467-1471 (2024). [Online] Available: https://doi.org/10.47974/jdmsc-1828.
[11] H. Ahmed, M. Ruby Salestina, and Anwar Alwardi, “Domination topological indices and their polynomials of a firefly graph,” J. Discrete Math. Sci. Cryptogr., vol. 24, no. 2, pp. 325-341 (2021). [Online] Available: https://doi.org/10.1080/09720529.2021.1882155.
[12] S. Hussain, F. Afzal, D. Afzal, M. R. Farahani, M.Cancan, and S. Ediz, “Theoretical study of benzene ring embedded in P-type surface in 2d network using some new degree based topological indices via M-polynomial,” Eurasian Chem. Commun., vol. 3, no. 3, pp. 180-186 (2021). [Online] Available: https://doi.org/10.22034/ecc.2021.272315.1134.
[13] S. Ahmad, H. M. A. Siddiqui, A. Ali, M.R. Farahani, M. Imran and I. N. Cangul. On Wiener index and Wiener polarity index of some polyomino chains,” J. Discrete Math. Sci. Cryptogr., vol. 22, no. 7, pp. 1151-1164 (2019), [Online] Available: https://doi.org/10.1080/09720529.2019.1688965.
[14] A.J.M. Khalaf, A.Q. Baig, M.R. Azhar, M. Imran and M.R. Farahani. The Eccentric Based Zagreb Indices of Carbon Graphite,” J. Discrete Math. Sci. Cryptogr., vol. 23, no. 6, pp. 1121-1137 (2020). [Online] Available: https://doi.org/10.1080/09720529.2020.1818448.
[15] M. Imran, A.A. E. Abunamous, D. Adi, S. H. Rafique, A.Q. Baig and M.R. Farahani. Eccentricity based topological indices of honeycomb networks,” J. Discrete Math. Sci. Cryptogr., vol. 22, no. 7, pp. 1199-1213 (2019). [Online] Available: https://doi.org/10.1080/09720529.2019.1691326.
[16] M. Imran, M.K. Siddiqui, S. Ahmad, M.F. Hanif, M.H. Muhammad and M.R. Farahani. Topological properties of Benzenoid, phenylenes and nanostar dendrimers,” J. Discrete Math. Sci. Cryptogr., vol. 22, no. 7, pp. 1229-1248 (2019), [Online] Available: https://doi.org/10.1080/09720529.2019.1701267.
[17] A.J.M. Khalaf, M.F. Hanif, M.K. Siddiqui and M.R. Farahani. On degree based topological indices of bridge graphs,” J. Discrete Math. Sci. Cryptogr., vol. 23, no. 6, pp. 1139-1156 (2020), [Online] Available: https://doi.org/10.1080/09720529.2020.1822040.

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