On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes

Let Γn and Λn be the n-dimensional Fibonacci cube and Lucas cube, respectively. The domination number γ of Fibonacci cubes and Lucas cubes is studied. In particular it is proved that γ(Λn) is bounded below by ⌈ Ln−2n n−3 ⌉ , where Ln is the n-th Lucas number. The 2-packing number ρ of these cubes is also studied. It is proved that ρ(Γn) is bounded below by 2 blg nc 2 −1 and the exact values of ...

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Independent Resolving Number of Fibonacci Cubes and Extended Fibonacci Cubes

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Independent Resolving Number of Fibonacci Cubes and Extended Fibonacci Cubes

A subset S of vertices in a graph G is said to be an independent set of G if each edge in the graph has at most one endpoint in S and a set W ( V is said to be a resolving set of G, if the vertices in G have distinct representations with respect to W. A resolving set W is said to be an independent resolving set, or an ir-set, if it is both resolving and independent. The minimum cardinality of W...

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Independent Resolving Number of Fibonacci Cubes and Extended Fibonacci Cubes

A subset S of vertices in a graph G is said to be an independent set of G if each edge in the graph has at most one endpoint in S and a set W ( V is said to be a resolving set of G, if the vertices in G have distinct representations with respect to W. A resolving set W is said to be an independent resolving set, or an ir-set, if it is both resolving and independent. The minimum cardinality of W...

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Independent Resolving Number of Fibonacci Cubes and Extended Fibonacci Cubes

A subset S of vertices in a graph G is said to be an independent set of G if each edge in the graph has at most one endpoint in S and a set W ( V is said to be a resolving set of G, if the vertices in G have distinct representations with respect to W. A resolving set W is said to be an independent resolving set, or an ir-set, if it is both resolving and independent. The minimum cardinality of W...

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On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes

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