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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. $50$

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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