Agraph G is said to be regular when the degrees of its vertices are all equal. The common degree, say k, may be specified by calling it a k-regular graph. A 3-regular graph is said to be cubic. Cubic graphs have many properties and have played a key role in the four-color theorem.

Note. We have in a k-regular graph G with n vertices and m edges:

nk =2m

0-regular graph                                  1-regular graph                    2-regular graph                                   3-regular graph

Graph Theory  and Applications ,Jean-Claude Fournier, WILEY, page(34-35)