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Stability of (1,2)-total pitchfork domination | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 20، دوره 12، شماره 2، بهمن 2021، صفحه 265-274 اصل مقاله (504.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5035 | ||
| نویسندگان | ||
| Lamees K. Alzaki؛ Mohammed A. Abdlhusein* ؛ Amenah Kareem Yousif | ||
| Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq | ||
| تاریخ دریافت: 05 دی 1399، تاریخ بازنگری: 30 بهمن 1399، تاریخ پذیرش: 13 اسفند 1399 | ||
| چکیده | ||
| Let $G=(V, E)$ be a finite, simple, and undirected graph without 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 | ||
| مراجع | ||
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