Journal of Applied Mathematics

The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes

Shengzhang Ren

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Abstract

Let Γ n and Λ n be the n -dimensional Fibonacci cube and Lucas cube, respectively. Denote by Γ [ u n , k , z ] the subgraph of Γ n induced by the end-vertex u n , k , z that has no up-neighbor. In this paper, the number of end-vertices and domination number γ of Γ n and Λ n are studied. The formula of calculating the number of end-vertices is given and it is proved that γ ( Γ [ u n , k , z ] ) 2 k - 1 + 1 . Using these results, the larger bound on the domination number γ of Γ n and Λ n is determined.

Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 954738, 5 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305580

Digital Object Identifier
doi:10.1155/2014/954738

Mathematical Reviews number (MathSciNet)
MR3178979

Zentralblatt MATH identifier
07010806

Citation

Ren, Shengzhang. The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes. J. Appl. Math. 2014 (2014), Article ID 954738, 5 pages. doi:10.1155/2014/954738. https://projecteuclid.org/euclid.jam/1425305580


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