TY - JOUR
ID - 14753
TI - γ-Total Dominating Graphs of Lollipop, Umbrella, and Coconut Graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Eakawinrujee, Pannawat
AU - Trakultraipruk, Nantapath
AD - Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand
Y1 - 2024
PY - 2024
VL -
IS -
SP -
EP -
KW - total domination number
KW - total dominating graph
KW - gamma graph
DO - 10.22049/cco.2024.27940.1401
N2 - 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.
UR - https://comb-opt.azaruniv.ac.ir/article_14753.html
L1 - https://comb-opt.azaruniv.ac.ir/article_14753_71cea3971482682c6566a15610b10a6a.pdf
ER -