Transversal Total Domination in Graphs

Let \(G = (V, E)\) be a graph. A total dominating set of \(G\) which intersects every minimum total dominating set in \(G\) is called a transversal total dominating set. The minimum cardinality of a transversal total dominating set is called the transversal total domination number of G, denoted by \(\gamma_{tt}(G)\). In this paper, we begin to study this parameter. We calculate \(\gamma_{tt}(G)\) for some families of graphs. Further some bounds and relations with other domination parameters are obtained for \(\gamma_{tt}(G)\).