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Any value or interest in a formula that calculates (not look up) the 'integer order' of a given 'Independent Edge Set' OR given an 'Independent Set' calculates the 'integer order' on Complete Graphs? The Mappings of Perfect Matchings on a Complete Graph. Likewise for Cliques.

Example: n=8, k=2 vertices: 8 edge count: 28 perfect matchings: 105 vertice set: {1,2,3,4,5,6,7,8}

Order: Independent Edge Set (Perfect Matching) 1: {1,2}{3,4}{5,6}{7,8} 2: {1,2}{3,4}{5,7}{6,8} 3: {1,2}{3,4}{5,8}{6,7} … 105: {1,8}{2,7}{3,6}{4,5}

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  • $\begingroup$ Applies to any integer 'k' as well. ie: n=9,k=3. ({1,2,3}{4,5,6}{7,8,9}... $\endgroup$
    – Tim
    Nov 16, 2023 at 3:31
  • $\begingroup$ I ask because I can do this and have a proof that it is always accurate. And, I am not aware of the existence of anything similar. $\endgroup$
    – Tim
    Nov 16, 2023 at 3:37

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