Complete k-Partite Graph

A k-Partite Graph (i.e., a set of Vertices decomposed into $k$ disjoint sets such that no two Vertices within the same set are adjacent) such that every pair of Vertices in the $k$ sets are adjacent. If there are $p$, $q$, ..., $r$ Vertices in the $k$ sets, the complete $k$-partite graph is denoted $K_{p,q,\ldots,r}$. The above figure shows $K_{2,3,5}$.

See also Complete Graph, Complete k-Partite Graph, k-Partite Graph

References

Saaty, T. L. and Kainen, P. C. The Four-Color Problem: Assaults and Conquest. New York: Dover, p. 12, 1986.