Complete Tripartite Graph -- from Wolfram MathWorld
- ️Weisstein, Eric W.
- ️Wed Feb 20 2008
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.
Some special cases are summarized in the following table, some of which are illustrated above.
The number of Hamiltonian cycles in the graph
can be efficiently computed using a general complete
k-partite graph recurrence (Horák and Tovarek 1979). A closed-form
formula is also known (submitted as a problem, 2025).
See also
Complete Bipartite Graph, Complete Graph, Complete k-Partite Graph, Cone Graph, Fan Graph, k-Partite Graph
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References
--. Submitted problem to Amer. Math. Monthly. Feb. 2025. Chia, G. L. and Sim, K. A. "On the Skewness of the Join of Graphs."
Disc. Appl. Math. 161, 2405-2409, 2013.Horák, P.
and Tovarek, L. "On Hamiltonian Cycles of Complete -Partite Graphs." Math. Slovaca 29, 43-47,
1979.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Complete Tripartite Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CompleteTripartiteGraph.html