# DM-Graphs-Q4

A certain tree of order n has only vertices of degree 1 and degree 3. How many degree-3 vertices does the tree have?

(A). $\frac{n-1}{2}$

(B). $\frac{n-2}{2}$

(C). $\frac{n}{2}$

(D). $\frac{n-1}{3}$

reshown Jul 13, 2019

+1 vote
Ans is B.

I solved by taking counter examples

for n = 4 no of 3 degree vertex = 1

for n = 8 no of 3 degree vertex  = 3.
answered Jul 13, 2019 by (410 points)
an order of a tree and of a b-tree means the same?
No, we can not take a Binary tree here. Because if we take Binary tree then at least one vertex should have degree 2, which is not allowed.
So, here we should take the ternary tree.
I didn't mean binary tree @lakshmanpro20, I meant B-tree
https://en.wikipedia.org/wiki/B-tree

Actually, I am confused about the term order of the tree is 'n'  what does that mean?
Yes, we can take B-tree. Because here order is given.
order represents no of vertices.
(n-b)1 + 3b=2(n-1)[2*no. of edges in tree]

slove for b.

NOTE: edges in tree = n-1
answered Jan 2 by (5,850 points)