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arXiv · 1803.10486

Semitotal domination in trees

Wei Zhuang·Guoliang Hao
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Abstract

In this paper, we study a parameter that is squeezed between arguably the two important domination parameters, namely the domination number, $\gamma(G)$, and the total domination number, $\gamma_t(G)$. A set $S$ of vertices in $G$ is a semitotal dominating set of $G$ if it is a dominating set of $G$ and every vertex in S is within distance $2$ of another vertex of $S$. The semitotal domination number, $\gamma_{t2}(G)$, is the minimum cardinality of a semitotal dominating set of $G$. We observe that $\gamma(G)\leq \gamma_{t2}(G)\leq \gamma_t(G)$. In this paper, we give a lower bound for the semitotal domination number of trees and we characterize the extremal trees. In addition, we characterize trees with equal domination and semitotal domination numbers.

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Wei Zhuang, Guoliang Hao. 2018-03-28. Semitotal domination in trees. https://doi.org/10.23638/dmtcs-20-2-5

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