Nonexistence of certain edge-girth-regular graphs
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916183929782272 |
|---|---|
| author | Droogendijk, Leen |
| author_facet | Droogendijk, Leen |
| contents | Edge-girth-regular graphs (abbreviated as \emph{egr} graphs) are regular graphs in which every edge is contained in the same number of shortest cycles. We prove that there is no $3$-regular \emph{egr} graph with girth $7$ such that every edge is on exactly $6$ shortest cycles, and there is no $3$-regular \emph{egr} graph with girth $8$ such that every edge is on exactly $14$ shortest cycles. This was conjectured by Goedgebeur and Jooken. A few other unresolved cases are settled as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonexistence of certain edge-girth-regular graphs Droogendijk, Leen Combinatorics 05C35 (Primary) 05C38 (Secondary) Edge-girth-regular graphs (abbreviated as \emph{egr} graphs) are regular graphs in which every edge is contained in the same number of shortest cycles. We prove that there is no $3$-regular \emph{egr} graph with girth $7$ such that every edge is on exactly $6$ shortest cycles, and there is no $3$-regular \emph{egr} graph with girth $8$ such that every edge is on exactly $14$ shortest cycles. This was conjectured by Goedgebeur and Jooken. A few other unresolved cases are settled as well. |
| title | Nonexistence of certain edge-girth-regular graphs |
| topic | Combinatorics 05C35 (Primary) 05C38 (Secondary) |
| url | https://arxiv.org/abs/2403.20049 |