Ladder graph

A ladder graph is the Cartesian product of graphs of a graph path with the two-vertex complete graph $K_2$. Its two parallel rails are joined by a rung at each position. The doubly infinite ladder graph uses an infinite rail indexed by $\mathbb{Z}$.

The doubly infinite ladder graph has graph vertices $\mathbb{Z}\times \{0,1\}$, horizontal edges $\{(j,s),(j+1,s)\}$, and vertical edges $\{(j,0),(j,1)\}$.