Let $G$ be a finite graph and $K[G]$ the edge ring of $G$. Based on the
technique of Gr\"obner bases and initial ideals, it will be proved that, given
integers $f$ and $d$ with $7 \leq f \leq d$, there exists a finite graph $G$ on
$[d]={1,...,d}$ with $\depth K[G] = f$ and with $\Krull-dim K[G] = d$.