Directed graphs and its Boundary Vertices

Suppose that D = (V,E) is a strongly connected digraph. Let u, v ∈ V (D). The maximum distance md(u, v) is defined as md(u, v)=max{ −→ d (u, v), −→ d (v, u)} where −→ d (u, v) denote the length of a shortest directed u− v path in D. This is a metric. The boundary, contour, eccentric and peripheral sets of a strong digraph D are defined with respect to this metric. The main aim of this paper is to identify the above said metrically defined sets of a large strong digraph D in terms of its prime factor decomposition with respect to cartesian product.