#### The structure of $k$-Lucas cubes

Yıl: 2021 Cilt: 50 Sayı: 3 Sayfa Aralığı: 754 - 769 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

The structure of $k$-Lucas cubes

Öz:
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.
Anahtar Kelime: hypercube Lucas cube k-Fibonacci cube Lucas number Fibonacci cube Fibonacci number

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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 APA EĞECİOĞLU Ö, SAYGI E, SAYGI Z (2021). The structure of $k$-Lucas cubes. , 754 - 769. 10.15672/hujms.750244 Chicago EĞECİOĞLU Ömer,SAYGI ELİF,SAYGI Zülfükar The structure of $k$-Lucas cubes. (2021): 754 - 769. 10.15672/hujms.750244 MLA EĞECİOĞLU Ömer,SAYGI ELİF,SAYGI Zülfükar The structure of $k$-Lucas cubes. , 2021, ss.754 - 769. 10.15672/hujms.750244 AMA EĞECİOĞLU Ö,SAYGI E,SAYGI Z The structure of $k$-Lucas cubes. . 2021; 754 - 769. 10.15672/hujms.750244 Vancouver EĞECİOĞLU Ö,SAYGI E,SAYGI Z The structure of $k$-Lucas cubes. . 2021; 754 - 769. 10.15672/hujms.750244 IEEE EĞECİOĞLU Ö,SAYGI E,SAYGI Z "The structure of $k$-Lucas cubes." , ss.754 - 769, 2021. 10.15672/hujms.750244 ISNAD EĞECİOĞLU, Ömer vd. "The structure of $k$-Lucas cubes". (2021), 754-769. https://doi.org/10.15672/hujms.750244
 APA EĞECİOĞLU Ö, SAYGI E, SAYGI Z (2021). The structure of $k$-Lucas cubes. Hacettepe Journal of Mathematics and Statistics, 50(3), 754 - 769. 10.15672/hujms.750244 Chicago EĞECİOĞLU Ömer,SAYGI ELİF,SAYGI Zülfükar The structure of $k$-Lucas cubes. Hacettepe Journal of Mathematics and Statistics 50, no.3 (2021): 754 - 769. 10.15672/hujms.750244 MLA EĞECİOĞLU Ömer,SAYGI ELİF,SAYGI Zülfükar The structure of $k$-Lucas cubes. Hacettepe Journal of Mathematics and Statistics, vol.50, no.3, 2021, ss.754 - 769. 10.15672/hujms.750244 AMA EĞECİOĞLU Ö,SAYGI E,SAYGI Z The structure of $k$-Lucas cubes. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 754 - 769. 10.15672/hujms.750244 Vancouver EĞECİOĞLU Ö,SAYGI E,SAYGI Z The structure of $k$-Lucas cubes. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 754 - 769. 10.15672/hujms.750244 IEEE EĞECİOĞLU Ö,SAYGI E,SAYGI Z "The structure of $k$-Lucas cubes." Hacettepe Journal of Mathematics and Statistics, 50, ss.754 - 769, 2021. 10.15672/hujms.750244 ISNAD EĞECİOĞLU, Ömer vd. "The structure of $k$-Lucas cubes". Hacettepe Journal of Mathematics and Statistics 50/3 (2021), 754-769. https://doi.org/10.15672/hujms.750244