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Abstract: 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.
Keywords: Fibonacci cubes, Pell graphs, generating functions, center of graph, median graphs, k-Fibonacci sequence
Published in DiRROS: 08.04.2024; Views: 86; Downloads: 37
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