### Computational generation of assemblages of the incomplete graph of K and maximizing the assemblage pairing rounds.

#### Abstract

The objective of this research is to investigate both complete and incomplete graphs of K and work towards deriving an algorithm to generate A(G) where A is an assemblage of non-repeated rounds of the handshaking algorithm such that the assemblage has the greatest possible number of rounds. We hope to achieve this algorithm by both deriving it mathematically and computationally through an exhaustive search.

So far we have achieved the formulas for the theoretical maximum, or A(G), where G is a complete graph with K vertices. We have also achieve an algorithm that generates A(G) for a graph with K vertices such that K is less than 14. Further testing must be conducted for graphs with K vertices such that K is greater than 14.

It can be proven there exists some algorithm that generates A(G) for an incomplete graph of K vertices, and we are continuing to work toward deriving said algorithm. This research has been supported by Professor Paul Peck, and the Glenville State College research meetings.

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