Boundary vertices of Strongly Connected Digraphs with respect to `Sum Metric'

Suppose $D=(V,E)$ is a strongly connected digraph and $u,v\in V(D)$. Among the many metrics in graphs, the sum metric warrants further exploration. The sum distance $sd(u,v)$ defined as $sd(u,v)=\overrightarrow{d}(u,v)+\overrightarrow{d}(v,u)$ is a metric where $\overrightarrow{d}(u,v)$ denotes the length of the shortest directed $u-v$ path in $D$. The four main boundary vertices in the digraphs are boundary vertices, contour vertices, eccentric vertices'', and peripheral vertices’’ and their relationships have been studied. Also, an attempt is made to study the boundary-type sets of corona product of (di)graphs. The center of the corona product of two strongly connected digraphs is established. All the boundary-type sets and the center of the corona product are established in terms of factor digraphs.