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

Abstract EN

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.