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γ-Total Dominating Graphs of Lollipop, Umbrella, and Coconut Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 11، شماره 1، خرداد 2026، صفحه 21-32 اصل مقاله (426.56 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.27940.1401 | ||
| نویسندگان | ||
| Pannawat Eakawinrujee1؛ Nantapath Trakultraipruk* 2 | ||
| 1Thammasat Secondary School, Faculty of Learning Sciences and Education, Thammasat University, Pathum Thani 12121, Thailand | ||
| 2Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| total domination number؛ total dominating graph؛ gamma graph | ||
| مراجع | ||
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