  The paper answers the question posed in a joint paper by A. A. Klyachko and
N. M. Luneva about the optimality of the estimate for the cost of symmetry in
graphs. The original estimate says that if n vertices can be removed from a
connected graph so that there is no connected subgraph of isomorphic $\Gamma$
left in it, then at most $n|V(\Gamma)|$ vertices that form a set invariant
under all automorphisms of the graph so that the graph does not contain a
subgraph isomorphic to $\Gamma$. We will prove that there exists a graph
$\Gamma$ for which this estimate is not optimal.
