Recall that Kn is the simple undirected complete graph on n

Recall that K_n is the simple, undirected, complete graph on n vertices, where each vertex is connected by a single edge to every other vertex. Find an asymptotically tight bound on the number of edges of K_n.

Solution

number of edges in the complete graph on n vertices are n Choose2 = n(n-1)/2 = O(n^2)

since in complete graph between any two vertices there is exactly one edge.