Given an undirected graph = ( , ), a vertex ∈ is edge-vertex (ev) dominated by an edge ∈ if is either incident to or incident to an adjacent edge of . A set ⊆ is an edgevertex dominating set (referred to as ev-dominating set) of if every vertex of is ev-dominated by at least one edge of . The minimum cardinality of an ev-dominating set is the ev-domination number. The edge-vertex dominating set problem is to find a minimum ev-domination number. In this paper we prove that the ev-dominating set problem is NP-hard on unit disk graphs. We also prove that this problem admits a polynomial-time approximation scheme on unit disk graphs. Finally, we give a simple 5-factor linear-time approximation algorithm.
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