Transversal Total Domination in Graphs

Abstract

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 ${\gamma }_{tt}(G)$.