The Robertson graph is the unique 
-cage graph, illustrated
above in a number of embeddings. It has 19 vertices and 38 edges. It has girth 5,
diameter 3, chromatic number 3, and is a quartic
graph. The second of the embeddings above is due to Bondy and Murty (1976, p. 237),
while the third is a presumed minimal rectilinear crossing embedding (corresponding
to rectilinear crossing number 17)
due to Exoo.
The Robertson graph is implemented in the Wolfram Language as GraphData["RobertsonGraph"].
The Robertson graph has automorphism group order 24, possesses 5376 (directed) Hamiltonian cycles, and has 224 distinct order-1 generalized LCF notations, with none of higher order. Of these, 20 (illustrated above) have bilateral symmetry.
The Möbius-Kantor graph can be obtained as a subgraph of the Robertson graph by removing the three vertices and two edges illustrated above (pers. comm., E. Pegg, Jr., Oct. 27, 2025).
The Robertson graph satisfies the rhombus constraints and contains no known unit-distance forbidden subgraph, yet appears not to be a unit-distance. A number of embeddings found from different initial embeddings by minimizing the sum of square deviations from unit edge lengths until a local minimum was reached are illustrated above.
