Boundary vertices of Strongly Connected Digraphs with respect to `Sum Metric'
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917036149440512 |
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| author | Anand, Bijo S. Changat, Manoj Narasimha-Shenoi, Prasanth G. Joseph, Mary Shalet Thottungal R, Mithra Narasimha-Shenoi, Prakash G. |
| author_facet | Anand, Bijo S. Changat, Manoj Narasimha-Shenoi, Prasanth G. Joseph, Mary Shalet Thottungal R, Mithra Narasimha-Shenoi, Prakash G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20226 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary vertices of Strongly Connected Digraphs with respect to `Sum Metric' Anand, Bijo S. Changat, Manoj Narasimha-Shenoi, Prasanth G. Joseph, Mary Shalet Thottungal R, Mithra Narasimha-Shenoi, Prakash G. Combinatorics Discrete Mathematics 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. |
| title | Boundary vertices of Strongly Connected Digraphs with respect to `Sum Metric' |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2510.20226 |