In the mathematical field of graph theory, the **ladder graph** *L*_{n} is a planar undirected graph with *2n* vertices and *n+2(n-1)* edges.

The ladder graph can be obtained as the Cartesian product of two path graphs, one of which has only one edge: *L*_{n,1} = *P*_{n} × *P*_{1}. Adding two more crossed edges connecting the four degree-two vertices of a ladder graph produces a cubic graph, the Möbius ladder.

By construction, the ladder graph L_{n} is isomorphic to the grid graph *G*_{2,n} and looks like a ladder with *n* rungs. It is Hamiltonian with girth 4 (if *n>1*) and chromatic index 3 (if *n>2*).

The chromatic number of the ladder graph is 2 and its chromatic polynomial is
(
x
−
1
)
x
(
x
2
−
3
x
+
3
)
(
n
−
1
)
.

The **circular ladder graph** *CL*_{n} is the Cartesian product of a cycle of length *n≥3* and an edge. In symbols, *CL*_{n} = *C*_{n} × *P*_{1}. It has *2n* nodes and *3n* edges. Like the ladder graph, it is connected, planar and Hamiltonian, but it is bipartite if and only if *n* is even.