  The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the
least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$
labels that is preserved only by a trivial automorphism. The neighbourhood
corona of two graphs $G_1$ and $G_2$ is denoted by $G_1 \star G_2$ and is the
graph obtained by taking one copy of $G_1$ and $|V(G_1)|$ copies of $G_2$, and
joining the neighbours of the $i$th vertex of $G_1$ to every vertex in the
$i$th copy of $G_2$. In this paper we describe the automorphisms of the graph
$G_1\star G_2$. Using results on automorphisms, we study the distinguishing
number and the distinguishing index of $G_1\star G_2$. We obtain upper bounds
for $D(G_1\star G_2)$ and $D'(G_1\star G_2)$.
