GATE | GATE-CS-2003 | Question 36

How many perfect matchings are there in a complete graph of 6 vertices ?
(A) 15
(B) 24
(C) 30
(D) 60

Answer: (A)

Explanation: A perfect matching, every vertex of the graph is incident to exactly one edge of the matching. A perfect matching is therefore a matching of a graph containing n/2 edges, the largest possible, meaning perfect matchings are only possible on graphs with an even number of vertices. (Source

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