an:07040819
Zbl 1407.05172
Asplund, John; Davila, Randy; Krop, Elliot
A Vizing-type result for semi-total domination
EN
Discrete Appl. Math. 258, 8-12 (2019).
00430165
2019
j
05C69 05C76
Cartesian products; total domination number; semi-total domination number
Summary: 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 \(\gamma_{t 2}(G)\), 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 \(H\), \(\gamma_{t 2}(G \square H) \geq \frac{1}{3} \gamma_{t 2}(G) \gamma_{t 2}(H)\).