A Vizing-type result for semi-total domination
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Authors
Elliot Krop
John Asplund
Randy Davila
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Journal Article, Academic Journal
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Abstract
A set of vertices $S$ in a simple isolate-free graph $G$ is a semi-total dominating set of $G$ if it is a dominating set of $G$ and every vertex of $S$ is within distance 2 of another vertex of $S$. The semi-total domination number of $G$, denoted by $\gamma_{t2}(G)$, is the minimum cardinality of a semi-total dominating set of $G$. In this paper, we study semi-total domination of Cartesian products of graphs. Our main result establishes that for any graphs $G$ and $H$, $\gamma_{t2}(G\cart H)\ge \frac{1}{3}\gamma_{t2}(G)\gamma_{t2}(H)$.