If the number of edges in K500 is x and the number of edges in K502 is y, what is the

Step 1 of 3

Consider that the term \(K_{n}\) represents a complete graph having n vertices. A complete graph has exactly one edge between each pair of two vertices.

So the number of edges \(N_{e}\) in a graph having  vertices is equal to the number of pairs of two vertices from the  vertices,

                                                                       \(\begin{aligned}N_{e} & ={ }^{n} C_{2} \\ & =\frac{n !}{2 ! \cdot(n-2) !} \\ & =\frac{n \cdot(n-1) \cdot(n-2) !}{2 ! \cdot(n-2) !} \\ & =\frac{n \cdot(n-1)}{2}\end{aligned}\)