The maximum number of edges in a bipartite graph on 12 vertices is _________.

A bipartite graph $G = (V_1, V_2, E)$ partitions its set of vertices into two disjoint sets $V_1$ and $V_2$ such that $|V_1| + |V_2| = n = 12$.

The maximum number of edges in a complete bipartite graph $K_{m, n-m}$ is given by:

To maximize the product $m(12 - m)$, we choose $m = \frac{12}{2} = 6$.

Thus, the maximum number of edges is: