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The number of edges in a 'n' vertex complete graph is?

  1. $n ^{*} (n - 1) / 2$
  2. $n^{2}$
  3. $n ^{*} (n + 1) / 2$
  4. $n ^{*} (n + 1)$
in Graph Theory by Boss (30.8k points) | 1.6k views

1 Answer

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Best answer
Option a is right answer

In a complete graph each vertex is associated with all other vertes . They dont have self loop

So in Complete graph of n vertices

each vertex has a degree of n-1

Therfore n vertex will have n (n-1) degree....1

And we know that sum of degree of vertex = 2*edges

n*(n-1) = 2*e

e = n(n-1)/2
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