Definition: Regular Graph
An regular graph is an undirected graph, in which all vertices have the same degree.
A regular graph is called r-regular, or regular of degree r, if the degree of each vertex is r.
Example
The following figure demonstrates three different 3-regular graphs.

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References
Bibliography
- Aldous Joan M., Wilson Robin J.: "Graphs and Applications - An Introductory Approach", Springer, 2000