NIELIT 2022 April Scientist B | Section B | Question: 104

Question

A connected planar graph having $6$ vertices, $7$ edges contains ___________ regions.

• A. $15$
• B. $11$
• C. $3$
• D. $1$

Comments

By euler formula for connected graph ,

no of region =no of edge-no of vertices +2

                    =7-6+2=3

Answer 1

Given: for any planner graph:

• the number of vertices $(V)=6$
• the number of edges $(E)=7$
• the number of regions $(R/f)=?$

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

$\implies 6+R=7+2$

$\implies R=9-6=3$

So option (C) is correct.