  Let $\Lambda$ be a numerical semigroup and $I\subset \Lambda$ be an ideal of
$\Lambda$. The graph $G_I(\Lambda)$ assigned to an ideal $I$ of $\Lambda$ is a
graph with elements of $(\Lambda \setminus I)^*$ as vertices and any two
vertices $x,y$ are adjacent if and only if $x+y \in I$. In this paper we give a
complete characterization (up to isomorphism ) of the graph $G_I(\Lambda)$ to
be planar, where $I$ is an irreducible ideal of $\Lambda$. This will finally
characterize non planar graphs $G_I(\Lambda)$ corresponding to irreducible
ideal $I$.
