Prove that in any tree with n vertices, the number of nodes with degree 8 or...

Question

Question

Prove that in any tree with n vertices, the number of nodes with degree 8 or more is at most (n − 1)/4.

Answer 1

Answer #1

Solution:- Before starting your problem we should know some basic understanding of "Degree" , "Edge" and the relation between them.

Degree-

Degree of a node is the total number of children of that node.
Degree of a tree is the highest degree of a node among all the nodes in the tree.

Example-

Here,

Edge-

Example-

The relation between sum of degree and no of the node -

if the total number node is = N

then the sum of the degree is = 2(N-1).

I'm using contradiction method to prove this...

Let assume there are (n − 1)/4 nodes of degree 8 or more

then the sum of the degree is = = 2(N-1) or more.

Hence proved if there are n node in a tree then the number of nodes with degree 8 or more is at most (n − 1)/4.

Answer 2

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