Let $G$ be a graph of order $n$ such that for each vertex $v$ there are two associated vectors, $f_v, g_v\in R^n$, where $uv\in E(G)$ if and only if $\|f_u - f_v\|^2 \ge \|g_u-g_v\|^2$. 

[ISGCI][1] didn't discuss such a class. 

> Has this class of graphs been studied?  What are their properties?  Are they perhaps equivalent to some well-known graph class? 

Note that, if the scalers is associated to vertices, from [this post][2] I know the answer is the class of permutation graphs. Now, considering vectors (in $R^\ell$ for some $\ell \ge 2$) is a natural genralization. 


  [1]: http://www.graphclasses.org
  [2]: https://mathoverflow.net/questions/259503/have-this-generalization-of-indifference-graphs-been-studied-before=