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If a planner graph, having $25$ vertices divides the plane into $17$ different regions. Then how many edges are used to connect the vertices in this graph.

  1. $20$
  2. $30$
  3. $40$
  4. $50$
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4 votes
Best answer

We use Euler's formula for planar graphs :  $v-e+f=2$  where,

  • $v\;-$ no. of vertices,  
  • $e\;-$ no.of edges  and  
  • $f\;-$ no. of faces.  (Refer: Euler's Formula)


So,  $25-e+17=2$  $\Rightarrow$ $e=40$

Option C is correct.

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