What is the name of the diagram that graphically shows the sequence of activities and logic that controls the flow?

The diagram that graphically illustrates the sequence of activities and the logic controlling the flow is known as an activity diagram. This type of diagram is part of the Unified Modeling Language (UML) and is used to represent workflows of stepwise activities and actions with support for choice, iteration, and concurrency.

Activity diagrams are particularly useful for detailing the specific processes involved in a system, showcasing how different tasks relate to each other, and how they are sequenced over time. They provide a clear visual representation that helps stakeholders understand the various actions, branching, and decision points within a process or a workflow.

While other diagram types are also employed in system design and analysis, they serve different purposes. For instance, data flow diagrams focus on the flow of data within a system and how data moves between processes, whereas use case descriptions outline user interactions rather than sequences of operational activities. State machine diagrams depict the various states of an object and the transitions between those states, which is distinct from the sequenced activity flow captured in activity diagrams. Thus, the activity diagram is uniquely suited for conveying the sequential logic of activities, making it the correct answer in this context.