Ladder graph
In the mathematical field of graph theory, the ladder graph is a planar, undirected graph with vertices and edges.
The ladder graph can be obtained as the Cartesian [product of graphs|Cartesian product] of two path graphs, one of which has only one edge:.
Properties
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 and chromatic index 3.The chromatic number of the ladder graph is 2 and its chromatic polynomial is.
[Image:Ladder graphs.svg|thumb|450px|left|The ladder graphs L1, L2, L3, L4 and L5.]
Ladder rung graph
Sometimes the term "ladder graph" is used for the n × P2 ladder rung graph, which is the graph union of n copies of the path graph P2.[Image:Ladder rung graphs.svg|thumb|450px|left|The ladder rung graphs LR1, LR2, LR3, LR4, and LR5.]
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:
CL3 | CL4 | CL5 | CL6 | CL7 | CL8 |
Möbius ladder
Connecting the four 2-degree vertices of a standard ladder graph crosswise creates a cubic graph called a Möbius ladder.[Image:Moebius-ladder-16.svg|thumb|upright=1.35|left|Two views of the Möbius ladder M16.]