Year 2021, Volume 50 , Issue 3, Pages 754 - 769 2021-06-07

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.
hypercube, Fibonacci cube, Lucas cube, k-Fibonacci cube, Fibonacci number, Lucas number
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-6070-761X
Author: Ömer EĞECİOĞLU
Institution: University of California Santa Barbara
Country: United States


Orcid: 0000-0001-8811-4747
Author: Elif SAYGI
Institution: HACETTEPE UNIVERSITY
Country: Turkey


Orcid: 0000-0002-7575-3272
Author: Zülfükar SAYGI (Primary Author)
Institution: TOBB UNIVERSITY OF ECONOMICS AND TECHNOLOGY
Country: Turkey


Supporting Institution Tübitak
Project Number 117R032
Dates

Publication Date : June 7, 2021

Bibtex @research article { hujms750244, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {754 - 769}, doi = {10.15672/hujms.750244}, title = {The structure of \$k\$-Lucas cubes}, key = {cite}, author = {Eğecioğlu, Ömer and Saygı, Elif and Saygı, Zülfükar} }
APA Eğecioğlu, Ö , Saygı, E , Saygı, Z . (2021). The structure of $k$-Lucas cubes . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 754-769 . DOI: 10.15672/hujms.750244
MLA Eğecioğlu, Ö , Saygı, E , Saygı, Z . "The structure of $k$-Lucas cubes" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 754-769 <https://dergipark.org.tr/en/pub/hujms/issue/62731/750244>
Chicago Eğecioğlu, Ö , Saygı, E , Saygı, Z . "The structure of $k$-Lucas cubes". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 754-769
RIS TY - JOUR T1 - The structure of $k$-Lucas cubes AU - Ömer Eğecioğlu , Elif Saygı , Zülfükar Saygı Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.750244 DO - 10.15672/hujms.750244 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 754 EP - 769 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.750244 UR - https://doi.org/10.15672/hujms.750244 Y2 - 2020 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics The structure of $k$-Lucas cubes %A Ömer Eğecioğlu , Elif Saygı , Zülfükar Saygı %T The structure of $k$-Lucas cubes %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.750244 %U 10.15672/hujms.750244
ISNAD Eğecioğlu, Ömer , Saygı, Elif , Saygı, Zülfükar . "The structure of $k$-Lucas cubes". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 754-769 . https://doi.org/10.15672/hujms.750244
AMA Eğecioğlu Ö , Saygı E , Saygı Z . The structure of $k$-Lucas cubes. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 754-769.
Vancouver Eğecioğlu Ö , Saygı E , Saygı Z . The structure of $k$-Lucas cubes. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 754-769.
IEEE Ö. Eğecioğlu , E. Saygı and Z. Saygı , "The structure of $k$-Lucas cubes", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 754-769, Jun. 2021, doi:10.15672/hujms.750244