Ladder graph

By construction, the ladder graph Ln is isomorphic to the grid graph G2,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^2-3x+3)^{(n-1)}. Image:Ladder graph L8 2COL.svg|The chromatic number of the ladder graph is 2. ==Ladder rung graph==

Sometimes the term "ladder graph" is used for the nP2 ladder rung graph, which is the graph union of n copies of the path graph P2. == Circular ladder graph ==

The circular ladder graph CLn is constructible by connecting the four 2-degree vertices in a straight way, or by the Cartesian product of a cycle of length n ≥ 3 and an edge. In symbols, . 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. Circular ladder graph are the polyhedral graphs of prisms, so they are more commonly called prism graphs. Circular ladder graphs: == Möbius ladder ==

Connecting the four 2-degree vertices of a standard ladder graph crosswise creates a cubic graph called a Möbius ladder. == References ==