  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. A graphoidal cover of
$G$ is a collection $\psi$ of (not necessarily open) paths in $G$ such that
every path in $\psi$ has at least two vertices, every vertex of $G$ is an
internal vertex of at most one path in $\psi$ and every edge of $G$ is in
exactly one path in $\psi$. Let $\Omega(G,\psi)$ denote the intersection graph
of $\psi$. A graph $H$ is called a graphoidal graph, if there exists a graph
$G$ and a graphoidal cover $\psi$ of $G$ such that $H\cong \Omega (G, \psi)$.
In this paper, we study the distinguishing number and the distinguishing index
of the line graph and the graphoidal graph of a simple connected graph $G$.
