Transversal domination in double graphs

Let $G$ be any graph. A subset $S$ of vertices in $G$ is called a dominating set if each vertex not in $S$ is adjacent to at least one vertex in $S$. A dominating set $S$ is called a transversal dominating set if $S$ has nonempty intersection with every dominating set of minimum cardinality in $G$. The minimum cardinality of a transversal dominating set is called the transversal domination number denoted by $\gamma_{td}(G)$. In this paper, we are considering special types of graphs called double graphs obtained through a graph operation. We study the new domination parameter for these graphs. We calculate the exact value of domination and transversal domination number in double graphs of some standard class of graphs. Further, we also estimate some simple bounds for these parameters in terms of order of a graph.