Independent domination bondage number in graphs
*M. MehrabanCorresponding authorMazharmehraban2020@gmail.comDepartment of Mathematical Sciences Yazd UniversityYazd, 89195-741, Iran0009-0008-4012-723XView full profile → , Saeid Alikhanialikhani@yazd.ac.irDepartment of Mathematical Sciences Yazd UniversityYazd, 89195-741, Iran0000-0002-1801-203XView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Feb 2025
- Published Online:
- 11 Dec 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-2041
- Pages:
- 1–12
Abstract
Keywords
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References
[1] S. Amutha, K. Suriya Prabha, N. Anbazhagan, and P. Shanthi, “Split domination number of divisible dominating graphs,” J. Discrete Math. Sci. Cryptogr., vol. 24, no. 4, pp. 997–1006 (2021).
[2] Z. Alrikabi, A. Omran, and H. Al-Hwaeer, “Double captive domination number (DCDN),” J. Discrete Math. Sci. Cryptogr., vol. 27, no. 5, pp. 1–5 (2024).
[3] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of Domination in Graphs. New York, NY, USA: Marcel Dekker (1998).
[4] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Domination in Graphs: Advanced Topics. New York, NY, USA: Marcel Dekker (1998).
[5] D. P. Sumner, “Critical concepts in domination,” Discrete Math., vol. 86, pp. 33–46 (1990).
[6] N. Jafari Rad, E. Sharifi, and M. Krzywkowski, “Domination stability in graphs,” Discrete Math., vol. 339, pp. 1909–1914 (2016).
[7] M. Edward, A. Finbow, G. MacGillivray, and S. Nasserasr, “Independent domination bicritical graphs,” Australas. J. Comb., vol. 72, pp. 446–471 (2018).
[8] J. Fulman, D. Hanson, and G. MacGillivray, “Vertex domination-critical graphs,” Networks, vol. 25, no. 2, pp. 41–43 (1995).
[9] Z. Li, Z. Shao, and S.-j. Xu, “2-rainbow domination stability of graphs,” J. Comb. Optim., vol. 38, pp. 836–845 (2019).
[10] M. Mehryar and S. Alikhani, “Weakly connected domination stability in graphs,” Adv. Appl. Math. Sci., vol. 16, no. 2, pp. 79–87 (2016).
[11] D. P. Sumner and P. Blitch, “Domination critical graphs,” J. Combin. Theory Ser. B, vol. 34, pp. 65–76 (1983).
[12] P. Wu, H. Jiang, S. Nazari-Moghaddam, S. M. Sheikholeslami, Z. Shao, and L. Volkmann, “Independent domination stable trees and unicyclic graphs,” Mathematics, vol. 7, no. 820, pp. 1–17 (2019).
[13] S. Alikhani, M. Mehraban, A. Zakharov, and H. R. Golmohammadi, “Independent domination stability in graphs,” J. Discrete Math. Sci. Cryptogr., to appear.
[14] W. Goddard and M. A. Henning, “Independent domination in graphs: A survey and recent results,” Discrete Math., vol. 313, no. 7, pp. 839–854 (2013).
[15] K. Kuenzel and D. F. Rall, “On independent domination in direct products,” Graphs Combin., vol. 39, no. 7 (2023), doi: 10.1007/s00373-022-02600-0.
[16] P. Erdős, A. Rényi, and V. T. Sós, “On a problem of graph theory,” Studia Sci. Math. Hungar., vol. 1, pp. 215–235 (1966).
[17] N. Ghanbari and S. Alikhani, “Sombor index of certain graphs,” Iranian J. Math. Chem., vol. 12, no. 1, pp. 27–37 (2021).
[18] S. Jahari and S. Alikhani, “On the independent domination polynomial of a graph,” Discrete Appl. Math., vol. 289, pp. 416–426 (2021).
