PERFECT MATCHING

Question

Consider complete graphs K5  and K6 . Let X5 and X6 are number of perfect matching of K5 and K6 respectively. Then X5 + X6 = ________.

Comments

15??

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Yes it is 15.

X5 = 0 and X6 =15

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For K6 = (6-1)(6-3)(6-5) = 5.3.1 = 15

For K5 = (5-1)(5-3)(5-5) = 0 (Not possible for odd no of vertices)

Hence 15 is correct answer

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@Ashwani Kumar 2 is it some kind of formula for k6?

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@Shubhanshu

Yes.. I wrote here plz check

https://gateoverflow.in/166671/perfect-matching-in-complete-graph#c166760

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K_2n=( 2n! ) / ( 2^n  *  n! )