Transversal Semitotal Domination Number in Graphs

A transversal semitotal dominating set in a graph G is a subset of vertices that intersects every minimal semitotal dominating set of \( G \) and itself forms a semitotal dominating set. Among all sets that intersect each semitotal dominating set of a graph \( G \), the one with the smallest cardinality defines a key parameter in the present study. This parameter is referred to as the transversal semitotal domination number and is denoted by \( γₜₜ₂(G) \). This paper investigates fundamental properties of this parameter in arbitrary graphs and determines exact values of \( γₜₜ₂(G) \) for several standard graph classes, including complete, star, wheel, cycle, path, and complete bipartite graphs.