University of Isfahan Transactions on Combinatorics 2251-8657 15 4 2025 11 29 Total and paired domination numbers of some wheel-related graphs 251 272 30046 10.22108/toc.2025.145488.2286 EN Pannawat Eakawinrujee Thammasat Secondary School, Faculty of Learning Sciences and Education, Thammasat University, Pathum Thani 12120, Thailand 0000-0003-1336-1019 Nantapath Trakultraipruk Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand Journal Article 2025 05 31 Let $G$ be a graph without isolated vertices. A total dominating set of $G$ is a set $D\subseteq V(G)$ such that every vertex of $G$ is adjacent to some vertex in $D$. A paired dominating set of $G$ is a total dominating set whose induced subgraph has a perfect matching. The total (paired) domination number of $G$ is the minimum cardinality of a total (paired) dominating set of $G$. In this paper, we determine the total and the paired domination numbers of some wheel-related graphs. We also give upper bounds on the total and the paired domination numbers of closed helm graphs and web graphs. Moreover, we determine the paired domination numbers of Jahangir graphs and correct some results on the total domination numbers presented by Mtarneh et al. (Malays. J. Math. Sci., 13(S) (2019) 113--121). https://toc.ui.ac.ir/article_30046_8038ac2fbfe3a857a62adfb3f38c4798.pdf