NIELIT 2017 DEC Scientific Assistant A - Section B: 38

Question

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.

• A. $20$
• B. $30$
• C. $40$
• D. $50$

Answer 1

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.