Transversal domination in graphs

Abstract

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