Some inner metric parameters of a digraph: Iterated line digraphs and integer sequences
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909303534780416 |
|---|---|
| author | Bong, N. H. Dalfó, C. Fiol, M. A. Závacká, D. |
| author_facet | Bong, N. H. Dalfó, C. Fiol, M. A. Závacká, D. |
| contents | In this paper, we first give a new result characterizing the strongly connected digraphs with a diameter equal to that of their line digraphs. Then, we introduce the concepts of the inner diameter and inner radius of a digraph and study their behaviors in its iterated line digraphs. Furthermore, we provide a method to characterize sequences of integers (corresponding to the inner diameter or the number of vertices of a digraph and its iterated line digraphs) that satisfy some conditions. Among other examples, we apply the method to the cyclic Kautz digraphs, square-free digraphs, and the subdigraphs of De Bruijn digraphs. Finally, we present some tables with new sequences that do not belong to The On-Line Encyclopedia of Integer Sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some inner metric parameters of a digraph: Iterated line digraphs and integer sequences Bong, N. H. Dalfó, C. Fiol, M. A. Závacká, D. Combinatorics In this paper, we first give a new result characterizing the strongly connected digraphs with a diameter equal to that of their line digraphs. Then, we introduce the concepts of the inner diameter and inner radius of a digraph and study their behaviors in its iterated line digraphs. Furthermore, we provide a method to characterize sequences of integers (corresponding to the inner diameter or the number of vertices of a digraph and its iterated line digraphs) that satisfy some conditions. Among other examples, we apply the method to the cyclic Kautz digraphs, square-free digraphs, and the subdigraphs of De Bruijn digraphs. Finally, we present some tables with new sequences that do not belong to The On-Line Encyclopedia of Integer Sequences. |
| title | Some inner metric parameters of a digraph: Iterated line digraphs and integer sequences |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.02125 |