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

For a given graph <f>G</f> a subset <f>X</f> of vertices of <f>G</f> is called a dominating (irredundant) set with respect to additive induced-hereditary property <f>P</f>, if the subgraph induced by <f>X</f> has the property <f>P</f> and <f>X</f> is a dominating (an irredundant) set. A set <f>S</f> is independent with respect to <f>P</f>, if <f>[S]∈P</f>.We give some properties of dominating, irredundant and independent sets with respect to <f>P</f> 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). [Copyright &y& Elsevier]