# tree

• Dec 11th 2012, 06:36 AM
prasum
tree
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 are there

i am getting 0 is it correct
• Dec 11th 2012, 06:42 AM
emakarov
Re: tree
Does the problem statement mean that there are no vertices with degrees higher than 4? Also, don't all leaves have degree 1?
• Dec 11th 2012, 07:03 AM
prasum
Re: tree
i am confused i had seen a formula

d1+d2+...dn=2n-2 where d is degree and n number of vertices
• Dec 11th 2012, 07:11 AM
emakarov
Re: tree
Quote:

Originally Posted by prasum

d1+d2+...dn=2n-2 where d is degree and n number of vertices

And how does it imply that there are no vertices of degree 1?
• Dec 11th 2012, 07:19 AM
prasum
Re: tree
i found the total vertices as 6+m where m is the no of vertices for degree 1
• Dec 11th 2012, 07:37 AM
emakarov
Re: tree
Quote:

Originally Posted by prasum
i found the total vertices as 6+m where m is the no of vertices for degree 1

Yes, and the sum of degrees is 2 * 2 + 1 * 3 + 3 * 4 + m = 19 + m. Now solve the equation 19 + m = 2(6 + m) - 2.