On the Möbius Ladders

Consider the graph Mn, where n = 2r ≥ 6, consisting of a polygon of length n and all n/2 chords joining opposite pairs of vertices. This graph has 2r vertices which we denote by 1, 2, 3,..., 2r, and the 3r (undirected) edges We call Mn the n-ladder, defined thus far only for n even. The three smallest n-ladders with n even are shown in Figure 1.