Tuples of homological invariants of edge ideals

Let $G$ be a graph and $I(G)$ its edge ideal. In this paper, we completely determine the tuples $(\dim R\mathrm{/}I(G),\text{depth}(R\mathrm{/}I(G)),\text{reg}(R\mathrm{/}I(G)))$ when the number of vertices is fixed for any graphs $G$.