A Vizing-type result for semi-total domination

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 γ 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, γ t2 (G□H)≥[Formula presented]γ t2 (G)γ t2 (H).