no of vertices in a graph

Question

The no of vertices in a graph containing 21 edges, 3 vertices of degree 4 and other vertices of degree 3 are:

a) 10

b) 13

c) 11

d) None

Sum of degrees of vertices= 2*no of edges

Let no of vertices=n

4*3+(n-3)*3= 42

n=13

But answer is given as 10..Plz explain how the answer is 10

Answer 1

13 is correct answer by the logic you have produced. Be confident, sometimes given answers are not correct!!

Answer 2

the answer should be 10.
in a tree
the degree of a node in tree is the number of child it has 

so if a node has degree 3, it has 3 child and 1parent(except root)

so 3 vertex of degree 4 contribute 3*5 in degree sum
lly remaining vertex of degree 3 contribute (x-3)*4

also we do -1 as root has no parent.

total degree sum=21*2=42.

3*5 + (x-3)*4 - 1 =42

gives x=10.