Summary: A subset \(D\) of a simple graph \(G=(V,E)\) is called a dominating set of \(G\) if for every vertex \(u\in V-D\), there exists \(v\in D\) such that \(u\) and \(v\) are adjacent. Several types of domination have been introduced. In T. W. Haynes et al. [Fundamentals of domination in graphs. New York, NY: Marcel Dekker, Inc. (1998; Zbl 0890.05002)], it is proposed that a type of domination is “fundamental” if every connected non trivial graph has a dominating set of this type. There are two fundamental varieties of domination namely, domination defined by its nature and domination defined interms of some property of the subgraph induced by the dominating set. In this paper a new domination belonging to the first type is introduced and studied.