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Prove or disprove the claim that a directed connected graph is strongly connected if every node...

Prove or disprove the claim that a directed connected graph is strongly connected if every node in the graph has at least one incoming edge and at least one outgoing edge.

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Answer #1

The claim that a directed connected graph is strongly connected if every node in the graph has at least one incoming edge and at least one outgoing edge is not always true.

Consider the below graph,

Every node has atleast one incoming and outgoing edge in the above graph.

A directed graph is strongly connected if there is a path between any two pair of vertices.

But here, we don't have path from node D to node B.

Thus, the statement claimed is not true. Hence, it is disapproved.

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