Edge-vertex domination in trees
Let [Formula: see text] be a finite simple graph. A vertex [Formula: see text] is edge-vertex dominated by an edge [Formula: see text] if [Formula: see text] is incident with [Formula: see text] or [Formula: see text] is incident with a vertex adjacent to [Formula: see text]. An edge-vertex dominating set of [Formula: see text] is a subset [Formula: see text] such that every vertex of [Formula: see text] is edge-vertex dominated by an edge of [Formula: see text]. The edge-vertex domination number [Formula: see text] is the minimum cardinality of an edge-vertex dominating set of [Formula: see text]. In this paper, we prove that [Formula: see text] for every tree [Formula: see text] of order [Formula: see text] with [Formula: see text] leaves, and we characterize the trees attaining each of the bounds.