The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes
Let Γn and Λn be the n-dimensional Fibonacci cube and Lucas cube, respectively. Denote by Γ[un,k,z] the subgraph of Γn induced by the end-vertex un,k,z that has no up-neighbor. In this paper, the number of end-vertices and domination number γ of Γn and Λn are studied. The formula of calculating the...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/954738 |
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| Summary: | Let Γn and Λn be the n-dimensional Fibonacci cube and Lucas cube, respectively. Denote by Γ[un,k,z] the subgraph of Γn induced by the end-vertex un,k,z that has no up-neighbor. In this paper, the number of end-vertices and domination number γ of Γn and Λn are studied. The formula of calculating the number of end-vertices is given and it is proved that γ(Γ[un,k,z])≤2k-1+1. Using these results, the larger bound on the domination number γ of Γn and Λn is determined. |
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| ISSN: | 1110-757X 1687-0042 |