- Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol: 21 Issue: 3
- Upper Bounds on the Domination and Total Domination Number of Fibonacci Cubes
Upper Bounds on the Domination and Total Domination Number of Fibonacci Cubes
Authors : Elif Saygi
Pages : 782-785
Doi:10.19113/sdufbed.05851
View : 7 | Download : 4
Publication Date : 2017-08-08
Article Type : Other
Abstract :One of the basic model for interconnection networks is the $n$-dimensional hypercube graph $Q_n$ and the vertices of $Q_n$ are represented by all binary strings of length $n$. The Fibonacci cube $\Gamma_n$ of dimension $n$ is a subgraph of $Q_n$, where the vertices correspond to those without two consecutive 1s in their string representation. In this paper, we deal with the domination number and the total domination number of Fibonacci cubes. First we obtain upper bounds on the domination number of $\Gamma_n$ for $n\ge 13$. Then using these result we obtain upper bounds on the total domination number of $\Gamma_n$ for $n\ge 14$ and we see that these upper bounds improve the bounds given in [1].Keywords : Fibonacci cube, Domination number, Total domination number