What is the minimum number of edges in a strongly connected digraph on $n$ vertices? At first I thought it would be $n(n-1)$ but that is not the minimum number of edges. I would be glad if someone could help me with this.
Edges in strongly connected digraph
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combinatorics
graph-theory
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0More context is needed. What did you try? Why did your answer fail? – 2017-01-06
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0A cyclic digraph with n-edges will do. – 2017-01-06
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0why did you think $n(n-2)$? that's all of the edges. – 2017-01-06
1 Answers
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The minimum number is $n$, because you can create a cycle with them that connects all the $n$ vertices in one strongly-connected component. With fewer than $n$ edges, you get at most a tree.