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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

The structure of $k$-Lucas cubes

Ömer EĞECİOĞLU
Elif Saygı
Zülfükar SAYGI
Pages
754–769
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We obtain a useful decomposition property of $k$-Lucas cubes which allows for the calculation of basic graph theoretic properties of this class: the number of edges, the average degree of a vertex, the number of hypercubes they contain, the diameter and the radius.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Fibonacci cubes and Lucas cubes have been studied as alternatives for the classical hypercube topology for interconnection networks.
📊
Key Findings & Data:These families of graphs have interesting graph theoretic and enumerative properties.
💡
Conclusion & Impact:We obtain a useful decomposition property of $k$-Lucas cubes which allows for the calculation of basic graph theoretic properties of this class: the number of edges, the average degree of a vertex, the number of hypercubes they contain, the diameter and the radius.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:hypercube · Fibonacci cube · Lucas cube

Abstract

Fibonacci cubes and Lucas cubes have been studied as alternatives for the classical hypercube topology for interconnection networks. These families of graphs have interesting graph theoretic and enumerative properties. Among the many generalization of Fibonacci cubes are $k$-Fibonacci cubes, which have the same number of vertices as Fibonacci cubes, but the edge sets determined by a parameter $k$. In this work, we consider $k$-Lucas cubes, which are obtained as subgraphs of $k$-Fibonacci cubes in the same way that Lucas cubes are obtained from Fibonacci cubes. We obtain a useful decomposition property of $k$-Lucas cubes which allows for the calculation of basic graph theoretic properties of this class: the number of edges, the average degree of a vertex, the number of hypercubes they contain, the diameter and the radius.

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Cite This Article

EĞECİOĞLU, Ö., Saygı, E., SAYGI, Z. (2022). The structure of $k$-Lucas cubes. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 754–769. https://ajindex.com/articles/529997

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