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.

The maximum number of edges in a complete undirected graph with n vertices is given by the formula n(n-1)/2.

Here's the step-by-step explanation:

1. In a complete graph, every pair of distinct vertices is connected by a unique edge.

2. For a single vertex in the graph, it can connect to (n-1) other vertices (since it can't connect to itself).

3. Since there are n such vertices, you might think there would be n*(n-1) edges. However, this counts every edge twice (once for each of its vertices), so we must divide by 2 to correct for this.

4. Therefore, the maximum number of edges is n(n-1)/2.