Cube graph
This article defines a particular undirected graph, i.e., the definition here determines the graph uniquely up to graph isomorphism.
View a complete list of particular undirected graphs
Definition
The term cube graph, sometimes cube or graph of a cube, refers to the cube in three-dimensional space viewed as a graph: the vertices are the vertices of the cube, and the edges are the edges of the cube.
Terminological confusion
This is not to be confused with cubic graph, a term used for a 3-regular graph. Note that the cube graph is cubic, but is not the only cubic graph.
Arithmetic functions
Size measures
| Function | Value | Explanation |
|---|---|---|
| size of vertex set | 8 | |
| size of edge set | 12 |
Numerical invariants associated with vertices
Since the graph is a vertex-transitive graph, any numerical invariant associated to a vertex must be equal on all vertices of the graph. Below are listed some of these invariants:
| Function | Value | Explanation |
|---|---|---|
| degree of a vertex | 3 | |
| eccentricity of a vertex | 3 |
Other numerical invariants
| Function | Value | Explanation |
|---|---|---|
| clique number | 2 | |
| independence number | 4 | |
| chromatic number | 2 | |
| radius of a graph | 3 | Due to vertex-transitivity, the radius equals the eccentricity of any vertex, which has been computed above. |
| diameter of a graph | 3 | Due to vertex-transitivity, the radius equals the eccentricity of any vertex, which has been computed above. |
| odd girth | infinite | |
| even girth | 4 | |
| girth of a graph | 4 |
Graph properties
| Property | Satisfied? | Explanation |
|---|---|---|
| connected graph | Yes | |
| regular graph | Yes | all vertices have degree three |
| vertex-transitive graph | Yes | |
| cubic graph | Yes | all vertices have degree three |
| edge-transitive graph | Yes | |
| symmetric graph | Yes | |
| distance-transitive graph | Yes | |
| bridgeless graph | Yes | |
| strongly regular graph | No |