On Vertex Covering Transversal Domination Number of Regular Graphs

A simple graph G = ( V , E ) is said to be r -regular if each vertex of G is of degree r . The vertex covering transversal domination number γ vct ( G ) is the minimum cardinality among all vertex covering transversal dominating sets of G . In this paper, we analyse this parameter on different kinds of regular graphs especially for Q n and H 3, n . Also we provide an upper bound for γ vct of a connected cubic graph of order n ≥ 8. Then we try to provide a more stronger relationship between γ and γ vct .