Depth of edge rings arising from finite graphs

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 $7\le f\le d$, there exists a finite graph $G$ on $[d]=1,\mathrm{.}\mathrm{.}\mathrm{.},d$ with $\text{depth}K[G]=f$ and with $\text{Krull}-dimK[G]=d$.