Notation for the scope of definition of a partial binary operation of a groupoid

Question

I have a groupoid ${\displaystyle (G,\ast )}$ with a partial binary operation ${\displaystyle *:G\times G\rightharpoonup G}$.

For every $(a,b)\displaystyle ∈G\times G$, $\displaystyle *$ is defined if $a ≠ b$, otherwise is not defined.

I would like to know what is the proper notation for giving the above detail on when the partial operation is defined and when is not in a condensed format.

Edit: Maybe $\displaystyle Dom(*)= \{(a,b)\displaystyle ∈G\times G\space| \space a ≠ b\}$?

Thank you