Given a graph $G=(V,E \subseteq V \times V)$, an edge set $D \subseteq E$ and a subset of nodes $W \subseteq V$, is there such thing as an established operator for the "restricted" set of $D$:
$$ \{ (u,v) | u \in W \vee v \in W\} \subseteq D $$
I did not find anything at wikipedia, but that does not necessarily mean something.
In case there is no such established operator, is $D | W$ acceptable/readable (i.e. has it some other obvious meaning in graph theory that I am not aware of?)
I'm not aware of any established notation for this, however, the notion of incidence is usually understood in a more general sense, that is, not only with regard to vertices/edges, but whole sets. Therefore, you could say that
$$\{(u,v) \in E \mid u∈W \lor v∈W\} \text{ is the subset of edges incident to }W.$$
Also, there is another similar notion, namely, the induced subgraph, i.e.
$$\{(u,v) \in E\mid u∈W \land v∈W\} \text{ is the set of edges induced by }W.$$
Given the two above, you can add that you intersect it with $D$. With some stretch, you can use function restriction notation $f|_\Omega$ (I have seen it used for induced subgraphs), but in any case, I would simply define the necessary operators, just to be clear (notation in graph theory varies a lot).
I hope this helps $\ddot\smile$