Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-2128Articles in Press20240423γ-Total Dominating Graphs of Lollipop, Umbrella, and Coconut Graphs1475310.22049/cco.2024.27940.1401ENPannawat EakawinrujeeDepartment of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand0000-0003-1336-1019Nantapath TrakultraiprukDepartment of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand0000-0002-2826-0176Journal Article20220729A total dominating set of a graph $G$ is a set $D\subseteq V(G)$ such that every vertex of $G$ is adjacent to some vertex in $D$. The total domination number $\gamma_{t}(G)$ of $G$ is the minimum cardinality of a total dominating set. The $\gamma$-total dominating graph $TD_{\gamma}(G)$ of $G$ is the graph whose vertices are minimum total dominating sets, and two minimum total dominating sets of $TD_{\gamma}(G)$ are adjacent if they differ by only one vertex. In this paper, we determine the total domination numbers of lollipop graphs, umbrella graphs, and coconut graphs, and especially their $\gamma$-total dominating graphs.https://comb-opt.azaruniv.ac.ir/article_14753_71cea3971482682c6566a15610b10a6a.pdf