Cartesian product of vertex sets of graph. 
Now what shall i call the operation $\otimes$ which is apparently different from cartesian product of the graphs $G$ and $H$ ?. Moreover, i want this operation to be different from Cartesian  product of the graphs. Shall i call the operation $\otimes$ as Cartesian product of vertex sets $V(G)$ and $V(H)$?

This is the graph join operation.
From this Math Stack Exchange question, the suggestion is to use the symbol $\nabla$ as in $G \nabla H$
