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An inverse triple effect domination in graphs | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 913-919 اصل مقاله (394.44 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5147 | ||
| 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: 18 بهمن 1399، تاریخ بازنگری: 06 فروردین 1400، تاریخ پذیرش: 14 فروردین 1400 | ||
| چکیده | ||
| In this paper, an inverse triple effect domination is introduced for any finite graph $G=(V, E)$ simple and undirected without isolated vertices. A subset $D^{-1}$ of $V-D$ is an inverse triple effect dominating set if every $v \in D^{-1}$ dominates exactly three vertices of $V-D^{-1}$. The inverse triple effect domination number $\gamma_{t e}^{-1}(G)$ is the minimum cardinality over all inverse triple effect dominating sets in $G$. Some results and properties on $\gamma_{t e}^{-1}(G)$ are given and proved. Under any conditions the graph satisfies $\gamma_{t e}(G)+\gamma_{t e}^{-1}(G)=n$ is studied. Lower and upper bounds for the size of a graph that has $\gamma_{t e}^{-1}(G)$ are putted in two cases when $D^{-1}=V-D$ and when $D^{-1} \neq V-D .$ Which properties of a vertex to be belongs to $D^{-1}$ or out of it are discussed. Then, $\gamma_{t e}^{-1}(G)$ is evaluated and proved for several graphs. | ||
| کلیدواژه‌ها | ||
| Dominating set؛ Triple effect domination؛ Inverse triple effect domination | ||
| مراجع | ||
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[1] M. A. Abdlhusein, Doubly connected bi-domination in graphs, Discrete Math. Algor. Appl. 13(2) (2021) 2150009. [2] M. A. Abdlhusein, Stability of inverse pitchfork domination, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 1009–1016. [3] M. A. Abdlhusein, Applying the (1,2)-pitchfork domination and its inverse on some special graphs, Bol. Soc. Paran. Mat. (accepted to appear)(2021). [4] M. A. Abdlhusein and M. N. Al-Harere, Total pitchfork domination and its inverse in graphs, Discrete Math. Algor. Appl (2020) 2150038. [5] M. A. Abdlhusein and M. N. Al-Harere, New parameter of inverse domination in graphs, Indian Journal of Pure and Applied Mathematics, (accepted to appear) (2021). [6] M. A. Abdlhusein and M. N. Al-Harere, Doubly connected pitchfork domination and its inverse in graphs, TWMS J. App. Eng. Math., (accepted to appear) (2021). [7] 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(2) (2019) 51–55. [8] M. A. Abdlhusein and M. N. Al-Harere, Pitchfork domination and its inverse for complement graphs, Proc. Inst. Appl. Math. 9(1) (2020) 13–17. [9] M. A. Abdlhusein and M. N. Al-Harere, Some modified types of pitchfork domination and its inverse, Bol. Soc. Paran. Mat. (accepted to appear) (2021). [10] Z. H. Abdulhasan and M. A. Abdlhusein, Triple effect domination in graphs, AIP Conference Proceedings , (accepted to appear) (2021). [11] M. N. Al-Harere and M. A. Abdlhusein, Pitchfork domination in graphs, Discrete Math. Algor. Appl. 12(2) (2020) 2050025. [12] M. N. Al-Harere, A. A. Omran and A. T. Breesam, Captive domination in graphs, Discrete Math. Algor. Appl. 12(6) (2020) 2050076. [13] L. K. Alzaki, M. A. Abdlhusein and A. K. Yousif, Stability of (1,2)-total pitchfork domination, Int. J. Nonlinear Anal. Appl. 12(2) (2021) 265–274 . [14] F. Harary Graph Theory, Addison-Wesley, Reading, MA, 1969. [15] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998. [16] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Domination in Graphs — Advanced Topics, Marcel Dekker Inc., 1998. [17] T. W. Haynes, M. A. Henning and P. Zhang, A survey of stratified domination in graphs, Discrete Math. 309 (2009) 5806–5819. [18] A. Khodkar, B. Samadi and H. R. Golmohammadi, (k, k, k) -Domination in graphs, J. Combin. Math. Combin. Comput. 98 (2016) 343–349. [19] C. Natarajan, S. K. Ayyaswamy and G. Sathiamoorthy, A note on hop domination number of some special families of graphs, Int. J. Pure Appl. Math. 119(12) (2018) 14165–14171. [20] O. Ore, Theory of Graphs, American Mathematical Society, Providence, RI, 1962. [21] M. S. Rahman, Basic Graph Theory, Springer, India, 2017. [22] S. J. Radhi, M. A. Abdlhusein and A. E. Hashoosh, The arrow domination in graphs, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 473–480. [23] H. J. Yousif and A. A. Omran, The split anti fuzzy domination in anti fuzzy graphs, J. Phys. Conf. Ser. (2020)1591012054. | ||
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