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 $\frac{n(n-1)}{2}$