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 γt2(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, γt2(G□H)≥13γt2(G)γt2(H).
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