Weighted Padovan graphs
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910620380561408 |
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| author | Chenoweth, Vesna Iršič Klavžar, Sandi Rus, Gregor Tan, Elif |
| author_facet | Chenoweth, Vesna Iršič Klavžar, Sandi Rus, Gregor Tan, Elif |
| contents | Weighted Padovan graphs $Φ^{n}_{k}$, $n \geq 1$, $\lfloor \frac{n}{2} \rfloor \leq k \leq \lfloor \frac{2n-2}{3} \rfloor$, are introduced as the graphs whose vertices are all Padovan words of length $n$ with $k$ $1$s, two vertices being adjacent if one can be obtained from the other by replacing exactly one $01$ with a $10$. By definition, $\sum_k |V(Φ^{n}_{k})|=P_{n+2}$, where $P_n$ is the $n$th Padovan number. Two families of graphs isomorphic to weighted Padovan graphs are presented. The order, the size, the degree, the diameter, the cube polynomial, and the automorphism group of weighted Padovan graphs are determined. It is also proved that they are median graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted Padovan graphs Chenoweth, Vesna Iršič Klavžar, Sandi Rus, Gregor Tan, Elif Combinatorics Weighted Padovan graphs $Φ^{n}_{k}$, $n \geq 1$, $\lfloor \frac{n}{2} \rfloor \leq k \leq \lfloor \frac{2n-2}{3} \rfloor$, are introduced as the graphs whose vertices are all Padovan words of length $n$ with $k$ $1$s, two vertices being adjacent if one can be obtained from the other by replacing exactly one $01$ with a $10$. By definition, $\sum_k |V(Φ^{n}_{k})|=P_{n+2}$, where $P_n$ is the $n$th Padovan number. Two families of graphs isomorphic to weighted Padovan graphs are presented. The order, the size, the degree, the diameter, the cube polynomial, and the automorphism group of weighted Padovan graphs are determined. It is also proved that they are median graphs. |
| title | Weighted Padovan graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.17318 |