Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 12 1 2021 05 01 Stability of Inverse Pitchfork Domination 1009 1016 4956 10.22075/ijnaa.2021.4956 EN Mohammed A. Abdlhusein Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq Journal Article 2020 10 01 There are few papers deals with stability of the inverse domination number in graphs by adding new edge to the graph or removing edge or vertex. Before this type of study, we need to know the stability of the domination number, then check the stability of the inverse domination. In this paper, the inverse pitchfork domination number $\gamma_{pf}^{-1}(G)$  is studied to be changing or not after adding or removing edge or removing vertex. Some conditions are putted on the graph to be affected or not with several results and examples. https://ijnaa.semnan.ac.ir/article_4956_034bf33163b63b47147524e23f004cc0.pdf