Stability of (۱,۲)-total pitchfork domination
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJNAA-12-2_020
تاریخ نمایه سازی: 11 آذر 1401
Abstract:
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 ۱\leq|N(t)\cap V-D|\leq۲ 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.
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Authors
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Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq
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Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq
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Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq