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A connected planar graph divides the plane into a number of regions. If the graph has eight vertices and these are linked by $13$ edges, then the number of regions is:

  1. $5$
  2. $6$
  3. $7$
  4. $8$
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Given: For any planner graph $G$

  • Number of  vertices $(V)=8$
  • Number of edges $(E)=13$
  • Number of regions/faces$(R/f)=?$

For any connected planner graph $ V+R=E+2$; 

$\implies 8+R=13+2$

$\implies R=15-8=7$

$\therefore$ the number of regions in given graph $G$ is $7$

Option $(C)$ is correct.

Answer:

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