Integer sets with prescribed pairwise differences being distinct (Q1775027)

For a graph \(G,\) denote by \(D(G)\) the smallest number \(k\) so that there is an injection \(f:V(G)\rightarrow \{1,2,\dots,k\}\) with the property that \( \left| f(u)-f(v)\right| \) are pairwise distinct for any edge \(uv\) of \(G.\) In the paper sharp bounds on the maximum value of \(D(G)\) that a graph \(G \) with given number of vertices and edges can have are given.