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

Shengzhang Ren

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: 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.

Date: 2014
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https://doi.org/10.1155/2014/954738

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:954738

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