  We consider the discrete Laplace operator $\Delta^{(N)}$ on
Erd\H{o}s--R\'{e}nyi random graphs with $N$ vertices and edge probability
$p/N$. We are interested in the limiting spectral properties of $\Delta^{(N)}$
as $N\to\infty$ in the subcritical regime $0<p<1$ where no giant cluster
emerges. We prove that in this limit the expectation value of the integrated
density of states of $\Delta^{(N)}$ exhibits a Lifshitz-tail behavior at the
lower spectral edge E=0.
