K-Graph

The Graph obtained by dividing a set of Vertices $\{1, \ldots, n\}$ into $k-1$ pairwise disjoint subsets with Vertices of degree $n_1$, ..., $n_{k-1}$, satisfying

$$n=n_1+\ldots+n_{k-1},$$

and with two Vertices joined Iff they lie in distinct Vertex sets. Such Graphs are denoted $K_{n_1, \ldots, n_k}$.

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