A Note on the Complementary Nil Domination Number of a Tree

A complementary nil dominating set of a graph G , is a set D of vertices of G such that D is a dominating set and V \ D is not a dominating set of G . The complementary nil domination number of a graph G , denoted by γ c n d ( G ) , is the minimum cardinality of a complementary nil dominating set of G . We characterize trees T of order n with l leaves, for which γ c n d ( T ) = n - l + 1 .