Edge-vertex domination in trees

Let G = (V,E) be a finite simple graph. A vertex v is an element of V is edge-vertex dominated by an edge e is an element of E if e is incident with v or e is incident with a vertex adjacent to v. An edge-vertex dominating set of G is a subset D subset of E such that every vertex of G is edge-vertex dominated by an edge of D. The edge-vertex domination number gamma ev(G) is the minimum cardinality of an edge-vertex dominating set of G. In this paper, we prove that n-l+2/4 <= gamma ev(T) <= n-1/2 for every tree T of order n >= 3 with l leaves, and we characterize the trees attaining each of the bounds.