ISRO-2013-76

Question

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

• A. $n ^{*} (n - 1) / 2$
• B. $n^{2}$
• C. $n ^{*} (n + 1) / 2$
• D. $n ^{*} (n + 1)$

Answer 1

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