ISRO 2024

Question

If there are five faces and nine vertices in an undirected planar graph, then number of edges is

1. 14
2. 6
3. 12
4. None of the above

Answer 1

 For a planner graph $G$ 

• Number of vertices $(V)= 9$
• Number of region/faces $(R/f)=5$
• Number of edges $(E)=?$

For any planner graph $V+F=E+2$

$\implies 9+5=E+2$

$\implies E=14-2=12$

$\therefore$ Number of edges in given graph $G$ is $12.$

Option $(C)$ is correct.