Definition:Regular Graph

Definition
Let $G = \left({V, E}\right)$ be a simple graph whose vertices all have the same degree $r$.

Then $G$ is called regular of degree $r$, or $r$-regular.

Also see

 * Definition:Edgeless Graph: a $0$-regular graph.
 * Definition:Cycle Graph: a $2$-regular graph.
 * Definition:Cubic Graph: a $3$-regular graph.