Suppose a database schedule $S$ involves transactions $T_1, \ldots, T_n$. Construct the precedence graph of $S$ with vertices representing the transactions and edges representing the conflicts. If $S$ is serializable, which one of the following orderings of the vertices of the precedence graph is guaranteed to yield a serial schedule? (A) Topological order (B) Depth-first order (C) Breadth-first order (D) Ascending order of transaction indices

If a schedule $S$ is conflict-serializable, its precedence (or serialization) graph is a Directed Acyclic Graph (DAG).

A topological sort of a DAG produces a linear ordering of its vertices such that for every directed edge $(T_i, T_j)$, transaction $T_i$ appears before $T_j$. Executing the transactions in this topological order produces a serial schedule that preserves all conflict dependencies, ensuring equivalence to schedule $S$.

Hence, the correct option is (A).