Perkel graph | |
---|---|
![]() Perkel graphs with 19-fold symmetry | |
Vertices | 57 |
Edges | 171 |
Radius | 3 |
Diameter | 3 |
Girth | 5 |
Automorphisms | 3420 |
Chromatic number | 3 |
Properties | Regular, distance-transitive |
Table of graphs and parameters |
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.
Perkel graph | |
---|---|
![]() Perkel graphs with 19-fold symmetry | |
Vertices | 57 |
Edges | 171 |
Radius | 3 |
Diameter | 3 |
Girth | 5 |
Automorphisms | 3420 |
Chromatic number | 3 |
Properties | Regular, distance-transitive |
Table of graphs and parameters |
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.