Is there a network with 50 arcs annnd one vertex?

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SUMMARY

A network can indeed consist of 50 arcs and a single vertex, provided that each arc is a loop originating and terminating at that vertex. This configuration allows for multiple arcs to connect back to the same point without the need for additional vertices. Conversely, it is not feasible to have 50 vertices connected by only one arc, as this would not satisfy the definition of a network where each vertex must be connected to at least one other vertex.

PREREQUISITES
  • Understanding of graph theory concepts, specifically vertices and arcs.
  • Familiarity with the definition of loops in a network.
  • Basic knowledge of network connectivity principles.
  • Ability to visualize and analyze simple network structures.
NEXT STEPS
  • Research the properties of directed and undirected graphs.
  • Explore the concept of loops in graph theory.
  • Learn about network connectivity and its implications in graph structures.
  • Investigate the relationship between vertices and edges in network design.
USEFUL FOR

Students studying graph theory, mathematicians exploring network structures, and anyone interested in the principles of connectivity in networks.

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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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