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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/954738 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832551795361054720 |
|---|---|
| author | Shengzhang Ren |
| author_facet | Shengzhang Ren |
| author_sort | Shengzhang Ren |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3e3cd9dbe1234691a91ef1fc11a9308f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3e3cd9dbe1234691a91ef1fc11a9308f2025-02-03T06:00:30ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/954738954738The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas CubesShengzhang Ren0School of Mathematics and Computer Science, Shaanxi University of Technology Hanzhong, Shaanxi 723001, ChinaLet 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.http://dx.doi.org/10.1155/2014/954738 |
| spellingShingle | Shengzhang Ren The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes Journal of Applied Mathematics |
| title | The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes |
| title_full | The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes |
| title_fullStr | The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes |
| title_full_unstemmed | The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes |
| title_short | The Larger Bound on the Domination Number of Fibonacci Cubes and Lucas Cubes |
| title_sort | larger bound on the domination number of fibonacci cubes and lucas cubes |
| url | http://dx.doi.org/10.1155/2014/954738 |
| work_keys_str_mv | AT shengzhangren thelargerboundonthedominationnumberoffibonaccicubesandlucascubes AT shengzhangren largerboundonthedominationnumberoffibonaccicubesandlucascubes |