Abstract
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.