VERTEX COVERING TRANSVERSAL DOMATIC NUMBER OF GRAPHS
A dominating set in a simple graph is said to be a vertex covering transversal dominating set if it intersects every minimum vertex covering set of G. The vertex covering transversal domination number is the minimum cardinality among all vertex covering transversal dominating sets of G. A partition of V is called a vertex covering transversal domatic partition of G if each is a vertex covering transversal dominating set. The maximum cardinality of a vertex covering transversal domatic partition of G is called the vertex covering transversal domatic number of G and is denoted by In this paper, we analyze this parameter for some standard graphs and also obtain its bounds.
dominating set, vertex covering transversal dominating set, vertex covering transversal domatic partition, vertex covering transversal domatic number.