For a graph property P and a graph G , a subset S of vertices of G is a P -set if the subgraph induced by S has the property P . The domination number with respect to the property P , denoted by γP(G) , is the minimum cardinality of a dominating P -set. Any property P satisfied by all edgeless graphs is called nondegenerate. For any graph G with n vertices and maximum degree ∆(G) , γP(G) ≤ n−∆(...