Octahedron 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 octahedron graph is an undirected graph whose vertices are the vertices of an octahedron and whose edges are the edges of the octahedron.

Alternatively, it can be defined as the 3-dimensional hyperoctahedron.

Arithmetic functions

Size measures

Function	Value	Explanation
size of vertex set	6	As $n$-dimensional hyperoctahedron, $n=3$: $2n=2(3)=6$
size of edge set	12	As $n$-dimensional hyperoctahedron, $n=3$: $2n(n-1)=2(3)(3-1)=12$

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	4	As $n$-dimensional hyperoctahedron, $n=3$: $2n-2=2(3)-2=4$
eccentricity of a vertex	2	As $n$-dimensional hypercube, $n=3$: 2 (independent of $n$)