Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2502.07520 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915146153066496 |
|---|---|
| author | Mollard, Michel |
| author_facet | Mollard, Michel |
| contents | The Fibonacci cube $Γ_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive $1$s. Recently Jianxin Wei and Yujun Yang introduced a one parameter generalization, Fibonacci $p$-cubes $Γ_n^p$, which are subgraphs of hypercubes induced by strings where there is at least $p$ consecutive $0$s between two $1$s. In this paper we first prove the expression conjectured by the authors for the cube polynomial of $Γ_n^p$. By a totally different method we then determine a generalization, the distance cube polynomial. We also complete the invariants investigated in the original paper by two new ones, the Mostar index $\mathit{Mo}(Γ_n^p)$ and the Irregularity $\irr(Γ_n^p)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07520 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some new results about Fibonacci p-cubes Mollard, Michel Combinatorics The Fibonacci cube $Γ_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive $1$s. Recently Jianxin Wei and Yujun Yang introduced a one parameter generalization, Fibonacci $p$-cubes $Γ_n^p$, which are subgraphs of hypercubes induced by strings where there is at least $p$ consecutive $0$s between two $1$s. In this paper we first prove the expression conjectured by the authors for the cube polynomial of $Γ_n^p$. By a totally different method we then determine a generalization, the distance cube polynomial. We also complete the invariants investigated in the original paper by two new ones, the Mostar index $\mathit{Mo}(Γ_n^p)$ and the Irregularity $\irr(Γ_n^p)$. |
| title | Some new results about Fibonacci p-cubes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2502.07520 |