## Journal of Applied Mathematics

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

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

#### Abstract

Let ${\mathrm{\Gamma}}_{n}$ and ${\mathrm{\Lambda}}_{n}$ be the $n$-dimensional Fibonacci cube and Lucas cube, respectively. Denote by $\mathrm{\Gamma}[{u}_{n,k,z}]$ the subgraph of ${\mathrm{\Gamma}}_{n}$ 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 $\gamma $ of ${\mathrm{\Gamma}}_{n}$ and ${\mathrm{\Lambda}}_{n}$ are studied. The formula of calculating the number of end-vertices is given and it is proved that $\gamma (\mathrm{\Gamma}[{u}_{n,k,z}])\le {2}^{k-1}+1$. Using these results, the larger bound on the domination number $\gamma $ of ${\mathrm{\Gamma}}_{n}$ and ${\mathrm{\Lambda}}_{n}$ 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