Final answer:
The maximum number of edges in a disconnected graph with 6 vertices is 15.
Step-by-step explanation:
The maximum number of edges in a disconnected graph is equal to the number of edges in a complete graph with the same number of vertices. In this case, the graph has 6 vertices, so the maximum number of edges is equal to the number of edges in a complete graph with 6 vertices.
The subject of the student's question is to find the maximum number of edges in a disconnected simple undirected graph with 6 vertices. To solve this, we need to consider the most extreme case of disconnection, which is having one vertex completely disconnected from the others.
The remaining 5 vertices can be fully connected (a complete graph), forming a maximum of 10 edges (since a complete graph with n vertices has n(n-1)/2 edges, which for 5 vertices is 5*4/2=10). Therefore, the maximum number of edges in a disconnected graph with 6 vertices would be 10, since adding any more edges would connect the isolated vertex, making the graph connected.
A complete graph with 6 vertices has $\binom{6}{2} = \frac{6!}{2!4!} = 15$ edges. Therefore, the maximum number of edges a disconnected graph with 6 vertices can have is 15.