What is the maximum number of edges in a complete undirected graph with n vertices?nn(n−1)/2n^2 2n

A complete undirected graph is a graph in which there is an edge between every pair of vertices.

The maximum number of edges in such a graph can be calculated using the formula:

n(n - 1) / 2

Here's the step-by-step calculation:

1. Consider that each vertex is connected to every other vertex. So, for 'n' vertices, each vertex would have 'n - 1' edges emanating from it.

2. Therefore, the total number of edges in the graph would be n * (n - 1).

3. However, this counts every edge twice (once for each vertex it connects), so we need to divide by 2 to get the correct number of edges.

So, the maximum number of edges in a complete undirected graph with n vertices is n(n - 1) / 2.