# Question regarding a directed graph with $n$ vertices and $n$ edges [closed]

If there exists a directed graph with $n$ vertices and $n$ edges, where each vertex has exactly one outgoing edge, and there exists multiple cycles (>=2), is it possible to form a graph where all the cycles are connected in one component?

## closed as off-topic by Henrik, Misha Lavrov, jvdhooft, Chris Custer, A. GoodierApr 11 '18 at 8:14

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• A connected graph with $n$ vertices and $n-1$ edges is a tree. – saulspatz Apr 11 '18 at 5:31
• Have you tried drawing such a graph to see if you can do it? – Misha Lavrov Apr 11 '18 at 6:19
• @saulspatz notice it's $n$ edges and not $n-1$ edges – Simon Park Apr 11 '18 at 6:43
• @Misha Lavrov I tried drawing many times but couldn't find an instance where two cycles could be in the same component, so I would like to believe it is not possible – Simon Park Apr 11 '18 at 6:44
• @SimonPark Yes, you add one edge to a tree. How many cycle does that create? – saulspatz Apr 11 '18 at 14:44