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2012-05-29T16:45:39Z

Created page with "{{particular undirected graph}} ==Definition== The '''octahedron graph''' is an undirected graph whose vertices are the vertices of an octahedron and whose edges are the..."

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{{particular undirected graph}}

==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===

{| class="sortable" border="1"
! Function !! Value !! Explanation
|-
| {{arithmetic function value|size of vertex set|6}} || As <math>n</math>-dimensional hyperoctahedron, <math>n = 3</math>: <math>2n = 2(3) = 6</math>
|-
| {{arithmetic function value|size of edge set|12}} || As <math>n</math>-dimensional hyperoctahedron, <math>n = 3</math>: <math>2n(n - 1) = 2(3)(3 - 1) = 12</math>
|}

===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:

{| class="sortable" border="1"
! Function !! Value !! Explanation
|-
| {{arithmetic function value|degree of a vertex|4}} || As <math>n</math>-dimensional hyperoctahedron, <math>n = 3</math>: <math>2n - 2 = 2(3) - 2 = 4</math>
|-
| {{arithmetic function value|eccentricity of a vertex|2}} || As <math>n</math>-dimensional hypercube, <math>n = 3</math>: 2 (independent of <math>n</math>)
|}

Octahedron graph - Revision history

Vipul: Created page with "{{particular undirected graph}} ==Definition== The '''octahedron graph''' is an undirected graph whose vertices are the vertices of an octahedron and whose edges are the..."