Cubical graph
Jump to navigation
Jump to search
| Cubical graph | |
|---|---|
.svg) | |
| Elements | |
| Vertices | 8 |
| Edges | 12 |
| Properties | |
| Girth | 4 |
| Radius | 3 |
| Diameter | 3 |
| Chromatic number | 2 |
| Chromatic index | 3 |
| Symmetry | |
| Vertex transitive | Yes |
| Edge transitive | Yes |
| Flag transitive | Yes |
| Distance transitive | Yes |
The cubical graph is the skeleton of the cube. It is distance-transitive cubic graph.
Related polytopes[edit | edit source]
The cubical graph can be embedded on the sphere as the cube. It can also be embedded on a torus as the regular skew polyhedron the Petrial cube.
Related graphs[edit | edit source]
The cubical graph is a graph in the infinite family of hypercube graphs. In that family it is Q 3 . The cubical graph is also the generalized Petersen graph GP (4, 1). It is one of seven symmetric generalized Petersen graphs.
Duals[edit | edit source]
With respects to its spherical embedding, the dual graph of the cubical graph is the octahedral graph, K 2,2,2 . With respects to its toroidal embedding its dual is a double cover of K 4 .
External links[edit | edit source]
- Wikipedia contributors. "Cubical graph".
- Weisstein, Eric W. "Cubical Graph" at MathWorld.