A complete tripartite graph is the k = 3 case of a complete k-partite graph. In other words, it is a tripartite graph (i.e., a set of graph vertices decomposed into three disjoint sets such that no two graph vertices within the same set are adjacent) such that every vertex of each set graph vertices is adjacent to every vertex in the other two sets. If there are p, q, and r graph vertices in the three sets, the complete tripartite graph (sometimes also called a complete trigraph) is denoted K_(p, q, r). Special classes are summarized in the following table.

complete bipartite graph | complete graph | complete k-partite graph | cone graph | fan graph | k-partite graph