A Graph is said to be regular of degree if all Local Degreesare the same number . Then
where is the number of Edges. The connected 3-regular graphs have been determined by G. Brinkmanup 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.