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A simple graph ( a graph without parallel edge or loops) with $n$ vertices and $k$ components can have at most

  1. $n$ edges
  2. $n-k$ edges
  3. $(n-k) (n-k+1)$ edges
  4. $(n-k) (n-k+1)/2$ edges
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3 Answers

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8 votes

Ans D)

graph with n vertices and k component has (n-k) ≤ e ≤(n-k)(n-k+1)/2 edges

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Take an example of a complete graph on 4 vertices, no. of components =1 and no. of edges =6 which is satisfied by option D.
Answer:

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