Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 04 25 Algorithmic complexity of three domination subdivision number problems in graphs 14937 10.22049/cco.2025.29896.2213 EN Deepak M. Bakal Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India Y.M. Borse Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India 0000-0002-0729-5433 B.N. Waphare Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India Journal Article 2024 07 19 The paired, total, and independent domination subdivision number of a graph $G$     is the minimum number of edges that must be subdivided, where each edge can be subdivided at most once, in order to increase the paired, total, and independent domination number, respectively. In this paper,     we prove that the corresponding decision problems for paired, total, and independent domination subdivision numbers are NP-hard, even when restricted to bipartite graphs. Additionally, we point out the error in the previous proof of $\mathrm{NP}$-hardness of the paired domination subdivision problem by Amjadi and Chellali  in  "Complexity of the paired domination subdivision problem" [Commun. Comb. Optim. 7 (2022), No.2, 177–182]. https://comb-opt.azaruniv.ac.ir/article_14937_03ba7538fe1bb1dc4078a68c715cc874.pdf