γ-Total Dominating Graphs of Lollipop, Umbrella, and Coconut Graphs

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Document Type : Original paper

Authors

Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand

Abstract

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.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 23 April 2024

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