Multiple choice

How many undirected graphs (not necessarily connected) can be constructed out of a given set $V={v_1, v_2, \dots v_n}$ of $n$ vertices?

  1. $\frac{n(n-1)} {2}$
  2. $2^n$
  3. $n!$
  4. $2^\frac{n(n-1)} {2} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given n vertices the various cases which are possible, no. connection, 1 connection it can be selected nc 2 ways, 2 connections & then (n − 1) connections to make complete graph $2^{^nC_2} $= $2^\frac{n(n-1)} {2} $

Keep practicing — related questions