I haven't seen people using dummy activities in this type of diagram. Is it true that they don't need dummy activities? What is the logic?
You need dummy tasks on activity on arrow network diagrams because there is no other way to show a predecessor task where that task results on two or more activities. On activity on node diagrams, like what is pictured, you do not need dummy tasks because you can have multiple arrows leaving a node to multiple successor tasks. Personally, I don't see any value in doing an activity on arrow diagram. But that's just my opinion.