Question

Prove that a tree with 14 pendants vertices the degree of every non pendant vertices is 4or 5 . show that the tree has 3 vertices of degree 4 and 2 vertices of degree 5

Answer 1

Answer:

Explanation:

You may use the formula, ∑deg(V)=2e∑deg(V)=2e.

Let the tree have n vertices. Then it has n-1 edges , being a tree.

Rest is easy, 2×4+3+2+(n−4)×1=2×(n−1)2×4+3+2+(n−4)×1=2×(n−1)

Or, 9 + n = 2n - 2

Or, n = 11.

Thus, The tree has 11 vertices (and 10 edges).

Answer 2

Prove that a tree with 14 pendants vertices the degree of every non pendant vertices is 4or 5 . show that the tree has 3 vertices of degree 4 and 2 vertices of degree 5