Domination, independence and irredundance with respect to additive induced-hereditary properties Original Research Article

For a given graph G a subset X of vertices of G is called a dominating (irredundant) set with respect to additive induced-hereditary property P, if the subgraph induced by X has the property P and X is a dominating (an irredundant) set. A set S is independent with respect to P, if [S]∈P. We give some properties of dominating, irredundant and independent sets with respect to P and some relations between corresponding graph invariants. This concept of domination and irredundance generalizes acyclic domination and acyclic irredundance given by Hedetniemi et al. (Discrete Math. 222 (2000) 151).