Residual property (mathematics)

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In the mathematical field of graph theory, the ladder graph Ln is a planar undirected graph with 2n vertices and n+2(n-1) edges.[1]

The ladder graph can be obtained as the Cartesian product of two path graphs, one of which has only one edge: Ln,1 = Pn × P1.[2][3] 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 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 (x1)x(x23x+3)(n1).

Gallery

The ladder graphs L1, L2, L3, L4 and L5.

References

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  2. Hosoya, H. and Harary, F. "On the Matching Properties of Three Fence Graphs." J. Math. Chem. 12, 211-218, 1993.
  3. Noy, M. and Ribó, A. "Recursively Constructible Families of Graphs." Adv. Appl. Math. 32, 350-363, 2004.