NIELIT 2017 July Scientist B (IT) - Section B: 8

Question

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:

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Comments

Option C (using Euler's formula   $v-e+f=2$)

Answer 1

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.