Directed Graphs

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I'm currently struggling with directed graphs. What does it mean when an allocated graph has a minimal vertex of p E P?

What's a minimal element?

What does it mean if something is acyclic and has a minimal element?

Any help would be greatly appreciated.

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A minimal vertex is a vertex with no edges leaving it.
Acyclic means does not have a cycle, a sequence of points a,b,c,.. z,a with an edge from a to b, from b to c and so on until an edge from z to a. A graph has a minimal vertex when it has a vertex which is a minimal vertex.