Complexity of Recognizing Multidistance Graphs in \(\mathbb{R}^d\)

We study the complexity of recognizing \(A\) -distance graphs in \(\mathbb{R}^d\) and prove that for all finite sets \(A\) such that any two elements of the set differ by a factor \(\ge2\) , the recognition problem for \(A\) -distance graphs is \(\mathrm{NP}\) -hard for any \(d \geq 3\) .