Cube graph

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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.

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