Perkel graph

Perkel graph

Perkel graphs with 19-fold symmetry
Vertices 57
Edges 171
Radius 3
Diameter 3
Girth 5
Automorphisms 3420
Properties Regular, distance-transitive

In mathematics, the Perkel graph, named after Manley Perkel, is a 6-regular graph with 57 vertices and 171 edges. It is the unique distance-regular graph with intersection array (6, 5, 2; 1, 1, 3).[1] The Perkel graph is also distance-transitive.

It is also the skeleton of an abstract regular polytope, the 57-cell.

References

  1. Coolsaet, K. and Degraer, J. "A Computer Assisted Proof of the Uniqueness of the Perkel Graph." Designs, Codes and Crypt. 34, 155–171, 2005.

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