Unlike the complete graph minus a perfect matching giving , which is known as the cocktail party graph, and the complete bipartite graph minus a perfect matching giving , which is known as the crown graph, the complete tripartite graph minus a perfect matching does not appear to have a special name.
is the 3-prism graph.
The numbers of perfect matchings in for , 1, ... are 1, 4, 825, 819242, 2243990201, 13077319842984, ... (OEIS A393180), which are given by the sum
See also
Cocktail Party Graph, Complete Tripartite Graph, Crown Graph, Perfect Matching
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References
Johnston, D.; Mark Kayll, P.; and Palmer, C. "Deranged Matchings: Proofs and Conjectures." 30 Oct 2022. https://arxiv.org/abs/2209.11319.Sloane, N. J. A. Sequence A393180 in "The On-Line Encyclopedia of Integer Sequences."
Cite this as:
Weisstein, Eric W. "Complete Tripartite Graph Minus Perfect Matching." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CompleteTripartiteGraphMinusPerfectMatching.html