UGC NET CSE | June 2009 | Part 2 | Question: 12

Question

The complete graph with four vertices has $k$ edges where $k$ is :

• A. $3$                  
• B. $4$     
• C. $5$                  
• D. $6$

Answer 1

Ans: D n(n-1)/2

Answer 2

A simple graph with $n$ vertex is called a complete graph $(K_n)$ if the degree of each vertex is $n−1$  means each vertex is attached to the remaining $n−1$ vertex.

The below figure represents  $K_4$ graph:

Clearly visible that $K_4$ graph having $6$ edges.

Option $D$ is correct.

Note: for $n$ vertices  in $K_n$ graph the number of edges is $\frac{n(n-1)}{2}$