Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2202.09853 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911957255192576 |
|---|---|
| author | Davis, Robert Jakovleski, Joakim Pan, Qizhe |
| author_facet | Davis, Robert Jakovleski, Joakim Pan, Qizhe |
| contents | The type-PQ adjacency polytope associated to a simple graph is a $0/1$-polytope containing valuable information about an underlying power network. Chen and the first author have recently demonstrated that, when the underlying graph $G$ is connected, the normalized volumes of the adjacency polytopes can be computed by counting sequences of nonnegative integers satisfying restrictions determined by $G$. This article builds upon their work, namely by showing that one of their main results -- the so-called "triangle recurrence" -- applies in a more general setting. Formulas for the normalized volumes when $G$ is obtained by deleting a path or a cycle from a complete graph are also established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_09853 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Normalized Volumes of Type-PQ Adjacency Polytopes for Certain Classes of Graphs Davis, Robert Jakovleski, Joakim Pan, Qizhe Combinatorics The type-PQ adjacency polytope associated to a simple graph is a $0/1$-polytope containing valuable information about an underlying power network. Chen and the first author have recently demonstrated that, when the underlying graph $G$ is connected, the normalized volumes of the adjacency polytopes can be computed by counting sequences of nonnegative integers satisfying restrictions determined by $G$. This article builds upon their work, namely by showing that one of their main results -- the so-called "triangle recurrence" -- applies in a more general setting. Formulas for the normalized volumes when $G$ is obtained by deleting a path or a cycle from a complete graph are also established. |
| title | Normalized Volumes of Type-PQ Adjacency Polytopes for Certain Classes of Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2202.09853 |