The schedule is serializable if the precedence graph has no cycles, indicating there's a serial ordering of transactions corresponding to the schedule without conflict.
The schedule is serializable if and only if the precedence graph has no cycles. To determine whether a given schedule is conflict serializable, one constructs a precedence graph (also known as a serialization graph) representing the schedule. Each transaction in the schedule is represented by a node, and edges are drawn between nodes if operations in those transactions conflict (that is, one operation reads or writes data that the other operation writes) and are not ordered in time in the schedule.
If the resulting graph has no cycles, then the schedule is conflict serializable, implying that there is some serial ordering of transactions that equates to the given schedule with respect to the final outcome of the data. However, if the graph does contain cycles, this indicates that there is no such ordering, and the schedule is not conflict serializable.