Independent partial domination

Abstract

For p ∈ (0 , 1] , a set S ⊆ V is said to p -dominate or partially dominate a graph G = ( V, E ) if | N [ S ] | | V | ≥ p . The minimum cardinality among all p -dominating sets is called the p -domination number and it is denoted by γ p ( G ) . Analogously, the independent partial domination ( i p ( G ) ) is introduced and studied here independently and in relation with the classical domination. Further, the partial independent set and the partial independence number β p ( G ) are defined and some of their properties are pre-sented. Finally, the partial domination chain is established as γ p ( G ) ≤ i p ( G ) ≤ β p ( G ) ≤ Γ p ( G ) . ,