beebeck1792 beebeck1792
  • 17-07-2019
  • Mathematics
contestada

A certain connected graph has 68 vertices and 72 edges. Does it have a circuit?

Respuesta :

presipao
presipao presipao
  • 31-07-2019

Answer:

Yes.

Step-by-step explanation:

If a graph G doesn't have a circuit, we must have that

[tex]|E(G)|=|V(G)|-1[/tex]

where [tex]|E(G)|[/tex] is the number of edges of the graph and [tex]|V(G)|[/tex] the number of vertices. However, in this case it holds that

[tex]|E(G)|=72>68=|V(G)|.[/tex]

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