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NIELIT 2018-70

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____ number of underlined graphs can be constructed using $V=(v1,v2, \dots,vn)$.

  1. $n^3$
  2. $2^{n(n-1)}/2$
  3. $n-1/2$
  4. $2^{(n-1)}/2$
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Graph with N vertices may have up to $N(N-1)/2$ edges (if loops aren't allowed). Now each edge have only 2 possibilities i.e. either Present or Absent. So overall number of possible graphs is  $2^{N(N-1)/2}$

SO OPTION B.

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→ With n vertices no. of possible edges = nC2
→ Each subset of these edges will form a graph.
→ Number of possible undirected graphs is 2(nC2) 2(n(n-1)/2)

Answer-B
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