Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 Articles in Press 2024 12 23 Exact double domination in the generalized Sierpinski graphs 5619 10.22060/ajmc.2024.23345.1251 EN Mahsa Khatibi Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran Ali Behtoei Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran Journal Article 2024 07 14 A subset $D$ of vertices of a simple graph ‎$‎G‎$ ‎is ‎an exact double dominating set if each vertex $v$ of $G$ is dominated by exactly two vertices of $D$‎, ‎i.e. $|N_G[v]\cap D|=2$‎, ‎in ‎which ‎‎$‎N_G[v]‎$ ‎is ‎the closed neighborhood of $v$ in ‎$‎G‎$‎.‎ The generalized Sierpi\'{n}ski graph $S(G,t)$ is a fractal-like graph that uses $G$ as a building block and can be constructed recursively in ‎$‎t‎$ ‎steps ‎from the base graph $G$. ‎In this paper we study and determine the existence of exact double dominating sets in generalized Sierpi\'nski graphs $S(P_n,t)$‎, ‎$S(C_n,t)$‎, ‎$S(K_{1,n},t)$ and $S(K_n,t)$‎.