Cartesian product of graphs

In graph theory, the cartesian product G $\square$ H of graphs G and H is a graph such that

• the vertex set of G $\square$ H is the cartesian product V(G) $\times$ V(H); and
• any two vertices (u,u') and (v,v') are adjacent in G $\square$ H if and only if either u = v and u' is adjacent with v' or u is adjacent with v and u' = v' .

Examples

• K₂ $\square$ K₂ = C₄ = Q₂, the square graph.
• K₂ $\square$ K₂$\square$ K₂ = Q₃, the cube graph.
• K₂ $\square$ K₂ $\square$ K₂$\square$ K₂ = Q₄, the tesseract graph.
• K₂ $\square$ C_n, the n-prism graph.