Boundary-type sets of strong product of directed graphs

Abstract

Let D = (V, E) be a strongly connected digraph and let u and v be two vertices in D. The maximum distance md(u, v) is defined as md(u, v) = max{d⃗(u, v),d⃗(v, u)}, where d⃗(u, v) denotes the length of a shortest directed u-v path in D. This is a metric. The boundary, contour, eccentricity and periphery sets of a strongly connected digraph D with respect to this metric have been defined. The boundary-type sets of the strong product of two digraphs is investigated in this article.