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?
Best Answer
I dont't know of a standard name, but it is $G \square K_2$, where $\square$ denotes the Cartesian product.