It can be embedded without crossings on a torus or projective plane, so it is also a toroidal graph.

[3] Möbius ladders play an important role in the theory of graph minors.

The earliest result of this type is a 1937 theorem of Klaus Wagner (part of a cluster of results known as Wagner's theorem) that graphs with no K5 minor can be formed by using clique-sum operations to combine planar graphs and the Möbius ladder M8.

It is an instance of an Andrásfai graph, a type of circulant graph in which the vertices can be arranged in a cycle and each vertex is connected to the other vertices whose positions differ by a number that is 1 (mod 3).

It can be drawn as a ladder graph with 4 rungs made cyclic on a topological Möbius strip.