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Stability and some results of triple effect domination | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 27، دوره 14، شماره 4، تیر 2023، صفحه 349-358 اصل مقاله (507.45 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6473 | ||
| نویسندگان | ||
| Zinah H. Abdulhasan؛ Mohammed A. Abdlhusein* | ||
| Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq | ||
| تاریخ دریافت: 27 بهمن 1400، تاریخ بازنگری: 29 اسفند 1400، تاریخ پذیرش: 07 اردیبهشت 1401 | ||
| چکیده | ||
| Let $G=(V, E)$ be a graph without isolated vertices. A subset $D \subseteq V$ is triple effect dominating set, if every vertex in $D$ dominates exactly three vertices of $V-D$. The triple effect domination number $\gamma_{t e}(G)$ is the minimum cardinality over all triple effect dominating sets in $G$. In this paper, the triple effect domination number $\gamma_{t e}(G)$ is studied to be changing or not after adding or deleting edge or deleting vertex. Some conditions are putted on the graph to be affected or not with several results and examples. Then, the triple effect domination and its inverse is applied on several graphs obtained from complement, join and corona operations. | ||
| کلیدواژهها | ||
| Dominating set؛ triple effect domination؛ inverse triple effect domination | ||
| مراجع | ||
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[1] M.A. Abdlhusein, New approach in graph domination, Ph. D. Thesis, University of Baghdad, Iraq, 2020. [2] M.A. Abdlhusein, Doubly connected bi-domination in graphs, Discrete Math. Algor. Appl. 13 (2021), no. 2, 2150009. [3] M.A. Abdlhusein, Stability of inverse pitchfork domination, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 1, 1009– 1016. [4] M.A. Abdlhusein, Applying the (1, 2)-pitchfork domination and its inverse on some special graphs, Bol. Soc. Paran. Mat. Accepted to appear, (2022). [5] M.A. Abdlhusein and M.N. Al-Harere, Total pitchfork domination and its inverse in graphs, Discrete Math. Algor. Appl. 13 (2021), no. 4, 2150038. [6] M.A. Abdlhusein and M.N. Al-Harere, New parameter of inverse domination in graphs, Indian J. Pure Appl. Math. 52 (2021), no. 1, 281–288. [7] M.A. Abdlhusein and M.N. Al-Harere, Doubly connected pitchfork domination and it’s inverse in graphs, TWMS J. App. and Eng. Math. 12 (2022), no. 1, 82-–91. [8] M.A. Abdlhusein and M.N. Al-Harere, Pitchfork domination and it’s inverse for corona and join operations in graphs, Proc. Int. Math. Sci. 1 (2019), no. 2, 51–55. [9] M.A. Abdlhusein and M.N. Al-Harere, Pitchfork domination and its inverse for complement graphs, Proc. Inst. Appl. Math. 9 (2020), no. 1, 13–17. [10] M.A. Abdlhusein and M.N. Al-Harere, Some modified types of pitchfork domination and its inverse, Bol. Soc. Paran. Math. 40 (2022), 1–9. [11] M. A. Abdlhusein and Z. H. Abdulhasan, Modified types of triple effect domination, reprinted, 2022. [12] M.A. Abdlhusein and S.J. Radhi, The arrow edge domination in graphs, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 2, 591–597. [13] Z.H. Abdulhasan and M.A. Abdlhusein, Triple effect domination in graphs, AIP Conf. Proc. 2386 (2022), 060013. [14] Z.H. Abdulhasan and M.A. Abdlhusein, An inverse triple effect domination in graphs, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 2, 913–919. [15] M.N. Al-Harere and M.A. Abdlhusein, Pitchfork domination in graphs, Discrete Math. Algor. Appl. 12 (2020), no. 2, 2050025. [16] L.K. Alzaki, M.A. Abdlhusein and A.K. Yousif, Stability of (1, 2)-total pitchfork domination, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 2, 265–274. [17] F. Harary, Graph theory, Addison-Wesley, Reading, MA, 1969. [18] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs, Marcel Dekker, Inc. New York, 1998. [19] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in graphs-advanced topics, Marcel Dekker, Inc., 1998. [20] T.W. Haynes, M.A. Henning, and P. Zhang, A survey of stratified domination in graphs, Discrete Math. 309 (2009), 5806–5819. [21] M.K. Idan and M.A. Abdlhusein,Some properties of discrete topological graph, IOP Conf. Proc. accepted to appear, 2022. [22] Z.N. Jweir and M.A. Abdlhusein, Appling some dominating parameters on the topological graph, IOP Conf. Proc. accepted to appear, (2022). [23] Z.N. Jweir and M.A. Abdlhusein, Some dominating results of the topological graph, Int. J. Nonlinear Anal. Appl. In press (2022) 10.22075/ijnaa.2022.6404. [24] Z.N. Jweir and M.A. Abdlhusein, Constructing new topological graph with several properties, reprinted, 2022. | ||
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