Boundary-type Sets of Strong Product of Directed Graphs

Abstract

Let $D=(V,E)$ be a strongly connected digraph and let $u,v\in V(D)$. The maximum distance $md(u,v)$ is defined as\\ $md(u,v)$=max\{$\overrightarrow{d}(u,v),\overrightarrow{d}(v,u)$\} where $\overrightarrow{d}(u,v)$ 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 $D$ with respect to this metric have been defined, and the above said metrically defined sets of a large strong digraph $D$ have been investigated in terms of the factors in its prime factor decomposition with respect to Cartesian product. In this paper we investigate about the above boundary-type sets of a strong digraph $D$ in terms of the factors in its prime factor decomposition with respect to strong product.