# Cubic graph

A simple graph in the called graph theory **cubic** or **3-regular** if all its nodes the degrees have third Cubic graphs are therefore regular graphs . Since 1-regular graphs only represent a pairing and 2-regular graphs decompose into disjoint cycles , cubic graphs are the simplest nontrivial cases of regular graphs.

## Number of cubic graphs

Since the sum of the node degrees in simple graphs must always be even, cubic graphs always have an even number of nodes .

n | # Connected cubic graphs with n nodes | # Cubic graphs with n nodes |
---|---|---|

2 | 0 | 0 |

4th | 1 | 1 |

6th | 2 | 2 |

8th | 5 | 6th |

10 | 19th | 21st |

12 | 85 | 94 |

## Examples

The full graph is the only cubic graph with 4 nodes.

The Petersen graph as an example of a cubic graph.

## Web links

**Commons : 3-regular graphs**- collection of images, videos and audio files

- Weisstein, Eric W .:
*Cubic Graph*. In:*MathWorld*(English).