The structure of $k$-Lucas cubes

Home Page
About
Submit A Journal
Submit A Conference
Submit Paper/Book
- Submit a Preprint
- Submit a Book
Contact

Hacettepe Journal of Mathematics and Statistics
Volume:50 Issue:3
The structure of $k$-Lucas cubes

The structure of $k$-Lucas cubes

Authors : Ömer EĞECİOĞLU, Elif SAYGI, Zülfükar SAYGI

Pages : 754-769

Doi:10.15672/hujms.750244

View : 22 | Download : 9

Publication Date : 2021-06-07

Article Type : Research Paper

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.
Keywords : hypercube, Fibonacci cube, Lucas cube, k Fibonacci cube, Fibonacci number, Lucas number

ORIGINAL ARTICLE URL

VIEW PAPER (PDF)

* There may have been changes in the journal, article,conference, book, preprint etc. informations. Therefore, it would be appropriate to follow the information on the official page of the source. The information here is shared for informational purposes. IAD is not responsible for incorrect or missing information.