Introduction:
An acyclic undirected graph is a graph that does not contain any cycles, which means there are no closed loops in the graph. In such a graph, the maximum number of edges can be determined based on the number of vertices.

Explanation:
To find the maximum number of edges in an acyclic undirected graph with n vertices, we need to consider that each vertex can be connected to all other vertices except itself and its adjacent vertices.

Maximum Number of Edges:
Let's consider a specific vertex in the graph. This vertex can be connected to all the remaining (n-1) vertices. However, it cannot be connected to itself or its adjacent vertices since it is an acyclic graph.

So, for each vertex, the maximum number of edges that can be added is (n-1) - 1 = n - 2.

Total Number of Edges:
Since there are n vertices in the graph, we need to sum up the number of edges for each vertex.

Total number of edges = n * (n - 2)

However, this counts each edge twice, once for each vertex it is connected to. Therefore, we need to divide the total number of edges by 2 to get the actual number of edges.

Total number of edges = n * (n - 2) / 2

Simplification:
Let's simplify the equation further:

n * (n - 2) / 2 = n * n / 2 - 2 * n / 2 = n^2 / 2 - n

Conclusion:
Hence, the maximum number of edges in an acyclic undirected graph with n vertices is n^2 / 2 - n, which can be approximated to n - 1.

Therefore, the correct answer is option 'A' (n - 1).