Graph of a Rel-morphism Let $F=(f;A;B)$ is a morphism of the category $\mathbf{Rel}$ (the category whose objects are sets and morphisms are defined as binary relations).
How to name and how to denote $f$ when we know $F$?
I propose to call $f$ the graph of $F$. Right name?
But how to denote it? Are there a standard notation?
I propose the following (non-standard) notation: $\mathrm{GR}\, F= f$.
 A: Graph of F is perfectly good.
I would write: $Graph(F)=f$, since GR in itself is a bit opaque as a name.
Edited after taking comments into account:
$\mathbf{Rel}$ is a bit atypical in the sense that it is named after its morphisms, while most categories are named after their objects (see MacLane's CWM chapter 1 notes). We can however form the category of arrows of $\mathbf{Rel}$, ie. $\mathbf{Rel}^\mathbf{2}$ (see CWM again) where the relations are the objects. So we could then write:
$U(F)=f$
Where $U:\mathbf{Rel}^\mathbf{2}\to \mathbf{Set}$ is the forgetful functor from $\mathbf{Rel}^\mathbf{2}$ to $\mathbf{Set}$ (since the graph of F is a set).
$\mathbf{2}$ is the category with 2 objects and just one morphism between them
Correction:
On second thought: graph of F is not a good name. That is because graph is normally meant to be an ordered pair (Wikipedia), while your $f$ is just a subset of $A \times B$. So I would simply call $f$ "the underlying set of $F$" and use the $U(F)=f$ notation to derive it
