Stability of (1,2)-total pitchfork domination

	Stability of (1,2)-total pitchfork domination
International Journal of Nonlinear Analysis and Applications
مقاله 20، دوره 16، شماره 4، تیر 2025، صفحه 233-240 اصل مقاله (541 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23235.2503
نویسندگان
Lamees K. Alzaki؛ Mohammed Abdali Abdlhusein^* ؛ Amenah Kareem Yousif
Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq
چکیده
Let $G=(V, E)$ be a finite, simple, and undirected graph without an isolated vertex. We define a dominating $D$ of $V(G)$ as a total pitchfork dominating set if $1\leq\|N(t)\cap V-D\|\leq2$ for every $t \in D$ such that $G[D]$ has no isolated vertex. In this paper, the effects of adding or removing an edge and removing a vertex from a graph are studied on the order of minimum total pitchfork dominating set $\gamma_{pf}^{t} (G)$ and the order of minimum inverse total pitchfork dominating set $\gamma_{pf}^{-t} (G)$. Where $\gamma_{pf}^{t} (G)$ is proved here to be increasing by adding an edge and decreasing by removing an edge, which are impossible cases in the ordinary total domination number.
کلیدواژه‌ها
total domination؛ stability of domination؛ pitchfork domination
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