 Cartesian product of graphs

For two graphs $G,H$, their Cartesian product of graphs has graph vertices $(g,h)\in V(G)\times V(H)$. Two graph vertices are adjacent if either their $G$ coordinates agree and their $H$ coordinates are adjacent, or conversely their $H$ coordinates agree and their $G$ coordinates are adjacent. The ladder graph is the product of a graph path with $K_2$.

The Cartesian product of two graphs \( G_1 = (V_1, E_1) \) and \( G_2 = (V_2, E_2) \) is a graph constructed by combining the vertices of the two graphs in a specific way.