Introduction:
A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that there are no edges between vertices within the same set. In other words, it is a graph that can be colored with two colors such that no two adjacent vertices have the same color. In this question, we are asked to find the maximum number of edges that can be present in a bipartite graph with 12 vertices.

Approach:
To find the maximum number of edges in a bipartite graph, we need to determine the maximum number of edges that can exist between the two sets of vertices. Let's assume the two sets are U and V.

Determining the sizes of sets U and V:
Since the graph has 12 vertices, we need to divide them into two sets, U and V. The sizes of these sets can vary, but their sum should be equal to the total number of vertices.

Let's consider the possible sizes of set U and calculate the corresponding size of set V:

- If set U has 1 vertex, set V will have 11 vertices.
- If set U has 2 vertices, set V will have 10 vertices.
- If set U has 3 vertices, set V will have 9 vertices.
- ...
- If set U has 11 vertices, set V will have 1 vertex.
- If set U has 12 vertices, set V will have 0 vertices.

Calculating the maximum number of edges:
The maximum number of edges can be calculated by multiplying the sizes of sets U and V. Since we want to find the maximum number of edges, we need to consider the scenario where one set has the maximum possible size and the other set has the minimum possible size.

In this case, when set U has 12 vertices and set V has 0 vertices, the maximum number of edges can be calculated as follows:

Maximum number of edges = size of set U * size of set V
= 12 * 0
= 0

Therefore, the maximum number of edges in a bipartite graph with 12 vertices is 0.

Conclusion:
The maximum number of edges in a bipartite graph on 12 vertices is 0.