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Please explain how perfect matching in given tree is 1?

Why not 3 with edges ab,ce,df?

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3 Answers

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I think they asked for the number of perfect matching. Here edge in Perfect matching is =3.

But {ab,ce, df} is the only possible perfect matching. So the number of perfect matching is 1

Hope this helps
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There is only one perfect matching possible for this graph which you mentioned in the question itself. {ab, ce, df}. This is the only set which represents perfect matching. Hence answer is 1. If two sets could represent the perfect matching for this graph, answer would be 2. Hope this helps.
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Option B

perfect matching is a matching that is used to cover every vertex in a graph

here  edges set {ab,ce,df} form the perfect matching 

here only one set of perfect matching is possible because we can not make more set like this which cover all the vertices but no vertices repeat (means every vertices exactly onces )

so no of perfect matching is 1

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atul_21 asked Dec 21, 2017
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I am not convinced by this. Please explain or please tell me the source from where I can clear this out.