Question

A tree has two vertices of degree 2, one vertex of degree 3, and three vertices of degree 4. How many vertices of degree 1 does it have?​

Answer 1

Answer:

A certain tree has two vertices of degree 4, one vertex of degree 3 and one vertex of degree 2. If the other vertices have degree 1, how many vertices are there in the graph?

n-3

-320

11

1Answer:11

Answer 2

Let number of vertices of degree 1 be k.

No of vertices = k + 2 + 1 + 1 = k +4  (we have two vertices of degree 4, one vertex of degree 3 and one vertex of degree 2)

No of edges = No of vertices -1 // As it is a tree

                   = k + 3

Applying  handshaking lemma

2 * 4 + 1 * 3 + 1 *2 + 1* k = 2 ( no edges ) = 2 * ( k +3)

=> 13 + k = 2k + 6

=> k = 7

So number of vertices = k +4 = 11

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