2025/10/23 by Bijo S. Anand, Manoj Changat, Anand, Bijo S. +9
Computer Science · Mathematics · #Graph Labeling and Dimension Problems #Advanced Graph Theory Research #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2510.20226
Suppose D = (V, E) is a strongly connected digraph and u, v ∈ 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) =\overrightarrowd(u, v)+\overrightarrowd(v, u) is a metric where \overrightarrowd(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.