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What is the value of the sum of the minimum in-degree and maximum out-degree of an Directed Acyclic Graph?

Question

What is the value of the sum of the minimum in-degree and maximum out-degree of a Directed Acyclic Graph?

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Solution

The value of the sum of the minimum in-degree and maximum out-degree of a Directed Acyclic Graph (DAG) can vary depending on the specific graph. However, we can make some general observations:

  1. In-degree of a node in a graph is the number of incoming edges to that node. In a DAG, the minimum in-degree is 0, because there can be nodes, known as source nodes, that do not have any incoming edges.

  2. Out-degree of a node in a graph is the number of outgoing edges from that node. In a DAG, the maximum out-degree can be (n-1), where n is the total number of nodes in the graph. This is because a node can have outgoing edges to every other node.

  3. Therefore, the sum of the minimum in-degree (which is 0) and the maximum out-degree (which is n-1) of a DAG is 0 + (n-1) = n-1.

So, the value of the sum of the minimum in-degree and maximum out-degree of a DAG is n-1.

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