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⊆V(G) such that every vertex of G is adjacent to some vertex in D. The total domination number γt(G) of G is the minimum cardinality of a total dominating set. The γ-total dominating graph TDγ(G) of G is the graph whose vertices are minimum total dominating sets, and two minimum total dominating sets of TDγ(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 γ-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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