Generalized Pell graphs
| Autor: | Iršič, Vesna, Klavžar, Sandi, Tan, Elif |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, generalized Pell graphs $\Pi _{n,k}$, $k\ge 2$, are introduced. The special case of $k=2$ are the Pell graphs $\Pi _{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of $\Pi _{n,k}$ and the generating function of its cube polynomial are determined. The center of $\Pi _{n,k}$ is explicitly described; if $k$ is even, then it induces the Fibonacci cube $\Gamma_{n}$. It is also shown that $\Pi _{n,k}$ is a median graph, and that $\Pi _{n,k}$ embeds into a Fibonacci cube. Comment: The title of this paper has been changed from the first version |
| Databáze: | arXiv |
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