فهرست نشریات علمی دسترسی آزاد ایران

‎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.