University of Kashan Mathematics Interdisciplinary Research 2538-3639 11 2 2026 06 01 Stability of 2-Domination Number of a Graph 113 124 115523 10.22052/mir.2025.257573.1540 EN Mazhar Mehraban Department of Mathematical Sciences, ‎Yazd University‎, ‎89195-741‎ ‎Yazd‎, ‎Iran Saeid Alikhani Department of Mathematical Sciences, ‎Yazd University‎, ‎89195-741‎ ‎Yazd‎, ‎Iran Journal Article 2025 09 13 ‎This paper delves into the stability of the 2-domination number in simple undirected graphs‎. ‎The 2-domination number of a graph G‎, ‎$\gamma_2(G)$‎, ‎represents the minimum size of a vertex subset where every other vertex in the graph is adjacent to at least two members of the subset‎. ‎We define the $2$-domination stability‎, ‎$st_{\gamma_2}(G)$‎, ‎as the smallest number of vertices whose removal causes a change in $\gamma_2(G)$‎. ‎Our primary contributions include computing this parameter for specific graphs‎, ‎establishing various bounds for this stability‎, ‎and determining its behavior under certain graph operations combining two graphs‎. https://mir.kashanu.ac.ir/article_115523_49a900eb52a696be092b9696b186f8c1.pdf