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 two path graphs, one of which has only one edge: .Hosoya, H. and Harary, F. "On the Matching Properties of Three Fence Graphs." J. Math. Chem. 12, 211-218, 1993.Noy, M. and Ribó, A. "Recursively Constructible Families of Graphs." Adv. Appl. Math. 32, 350-363, 2004.
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 (if n>1) and chromatic index 3 (if n>2).
The chromatic number of the ladder graph is 2 and its chromatic polynomial is .
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: CL3CL4CL5CL6CL7CL8
Möbius ladder
Connecting the four 2-degree vertices of a standard ladder graph crosswise creates a cubic graph called a Möbius ladder.
References