Let $G=(V\_1,E\_1)$ be a simple graph with vertex set $\{v\_1,v\_2,\ldots,v\_n\}$ and let $G'=(V\_2,E\_2)$ be another copy of $G$ with vertex set $\{u\_1,u\_2,\ldots,u\_n\}$. Assume $V\_1\cap V\_2= \emptyset$.


Let $H=(V,E)$ be a graph with $V=V\_1 \cup V\_2$ and $E=E\_1\cup E\_2\cup \{u\_1v\_1，u\_2v\_2, \ldots, v\_nv\_n\}$. It is obtained from $G$ by a graph operation as above. So, is there any name of this operation?



What's the name of the graph operation of connecting two copies of a graph with a perfect matching?
I dont't know of a standard name, but it is $G \square K\_2$, where $\square$ denotes the [Cartesian product](https://en.wikipedia.org/wiki/Cartesian_product_of_graphs).


