  Given an undirected graph $G=(V,E)$, a vertex $v\in V$ is edge-vertex (ev)
dominated by an edge $e\in E$ if $v$ is either incident to $e$ or incident to
an adjacent edge of $e$. A set $S^{ev}\subseteq E$ is an edge-vertex dominating
set (referred to as \textit{ev}-dominating set and in short as \textit{EVDS})
of $G$ if every vertex of $G$ is \textit{ev}-dominated by at least one edge of
$S^{ev}$. The minimum cardinality of an \textit{ev}-dominating set is the
\textit{ev}-domination number. The edge-vertex dominating set problem is to
find a minimum \textit{ev}-domination number. In this paper, we prove that the
\textit{ev}-dominating set problem is {\tt 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.
