From the tree Let's say ? = (?, ?) is undirected graph, with self-loops or no...
From the tree Let's say ? = (?, ?) is undirected graph, with self-loops or no parallel edges. And Let's say |?| = ? and |?| = ?.
Prove this thing by induction which 2? <= n2 − ? for all ? >= 1.(Its about the tree.)
Homework Answers
Ans:-
Base case:
n= 2, m= 1
Because we can connect two vertices with only one edge.
This proves
2*m<= n^2 - n
2*1<= 2^2 - 2
=> 2<= 2
The base case holds true.
inductive case:
for n= 3, we can have m= 2 for fulfilling the condition of a simple graph
which means
2*2 <= 3^2 - 3
=> 4<= 9 - 3
=> 4<= 6
Similarly for greater value of m and n the inequality
2*m<= n^2 - n will hold true.
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