NIELIT 2017 July Scientist B (IT) - Section B: 12

Question

Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is

• A. $6$
• B. $8$
• C. $9$
• D. $13$

Comments

Option B

Answer 1

Given: For any connected planner graph $G$

• Number of vertices $(v)=13$
• Number of edges $(e)=19$
• Number of regions/faces $(f)=?$

For any connected planner graph $v+f=e+2$

$\implies 13+f=19+2$

$\implies f=21-13$

$\implies f=8$

$\therefore$ the number of faces in given graph $G$ is $8$.

So option $(B)$ is correct.