Vertex covering transversal domination in graphs

A set $D subseteq V$ of vertices in a graph $G=(V, E)$ is called a dominating set if every vertex in $V-D$ is adjacent to a vertex in $D$. A set $C subseteq V$ of vertices in $G$ is called a vertex covering set if every edge of $G$ is incident to at least one vertex in $C$. Also $C$ is said to be a minimum vertex covering set if there is no other vertex covering set $C^prime$ such that $left|C'right| textless left|Cright|$. A dominating set which intersects every minimum vertex covering set in $G$ is called a vertex covering transversal dominating set. The minimum cardinality of a vertex covering transversal dominating set is called vertex covering transversal domination number of $G$ and is denoted by $gamma_{vct}(G)$. In this paper, we begin with an investigation of this parameter.