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

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