Is there a network with 50 arcs annnd one vertex?

AI Thread Summary
A network can indeed have 50 arcs and one vertex if all arcs are loops that start and end at that single vertex. This configuration allows for multiple connections while maintaining only one vertex. The discussion also raises the question of whether it is possible to have 50 vertices and only one arc. The feasibility of such a configuration is not established in the discussion. Overall, the concept of loops in network theory is central to understanding these configurations.
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Homework Statement


Is there a network with 50 arcs and one vertex?
 
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50 arcs and a single vertex? Well, yes, if every arc is a loop having vertex A as beginning and end!
 
HallsofIvy said:
50 arcs and a single vertex? Well, yes, if every arc is a loop having vertex A as beginning and end!

Thank you!

Is the reverse possible: to have 50 vertex and one arc?
 

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