Consider a simple undirected graph of 10 vertices. If the graph is disconnected, then the maximum number of edges it can have is ________.

For a simple undirected graph with $n$ vertices to be disconnected, it must have at least two connected components.

To maximize the number of edges while keeping the graph disconnected, one connected component should be a complete graph on $n-1$ vertices, and the remaining component should be an isolated vertex ($1$ vertex):

For $n = 10$:

Thus, the maximum number of edges is 36.