%0 Journal Article
%T γ-Total Dominating Graphs of Lollipop, Umbrella, and Coconut Graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Eakawinrujee, Pannawat
%A Trakultraipruk, Nantapath
%D 2024
%\ 04/23/2024
%V
%N
%P -
%! γ-Total Dominating Graphs of Lollipop, Umbrella, and Coconut Graphs
%K total domination number
%K total dominating graph
%K gamma graph
%R 10.22049/cco.2024.27940.1401
%X A 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.
%U https://comb-opt.azaruniv.ac.ir/article_14753_71cea3971482682c6566a15610b10a6a.pdf