A complete tripartite graph is the 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 , , and graph vertices in the three sets, the complete tripartite graph (sometimes also called a complete trigraph) is denoted .
Special classes are summarized in the following table.
special class | |
-fan graph | |
-fan graph | |
-cone graph |
Some special cases are summarized in the following table, some of which are illustrated above.
name | ||
3 | triangle graph | |
4 | diamond graph | |
5 | (3,2)-fan graph | |
5 | 5-wheel graph | |
6 | octahedral graph | |
6 | (3,3)-fan graph | |
6 | (4,2)-fan graph | |
7 | (4,3)-cone graph | |
7 | (4,3)-fan graph | |
7 | (5,2)-fan graph | |
8 | (4,4)-cone graph | |
8 | (5,3)-fan graph | |
9 | 9-circulant graph | |
9 | (4,5)-cone graph | |
12 | circulant graph | |
15 | circulant graph |