Regular Graph

A Graph is said to be regular of degree $r$ if all Local Degrees are the same number $r$. Then

$$E={\textstyle{1\over 2}}n r,$$

where $E$ is the number of Edges. The connected 3-regular graphs have been determined by G. Brinkman up to 24 Vertices.

See also Complete Graph, Completely Regular Graph, Local Degree, Superregular Graph

References

Chartrand, G. Introductory Graph Theory. New York: Dover, p. 29, 1985.