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# Möbius-Kantor graph

There is a unique cubic *symmetric* (i.e., both vertex- and
edge-transitive) graph on 16 vertices known as the Möbius-Kantor graph.
## Construction

The Möbius-Kantor graph is the bipartite point-line incidence graph
of the geometry with 8 points and 8 lines obtained by removing one
point from the affine plane AG(2,3) of order 3.
## Group

The group is GL(2,3).2 of order 96.
It is vertex- and edge-transitive, with vertex stabilizer Sym(3).
## Spectrum

The Möbius-Kantor graph has spectrum
±3^{1}, (±√3)^{4}, ±1^{3},
and is the unique graph with this spectrum.
## Distribution diagram

The graph is an antipodal 2-cover of the 3-cube.

It is the unique 2-cover of the 3-cube without quadrangles, cf. BCN 9.2.10.

One can add 8 edges and obtain the 4-cube (Coxeter).

## Reference

H. S. M. Coxeter,
*Self-dual configurations and regular graphs*,
Bull. Amer. Math. Soc. **56** (1950) 413-455.