GATE CSE 2021 | Set 1 | Question: 16

Question

In an undirected connected planar graph $G$, there are eight vertices and five faces. The number of edges in $G$ is _________.

Comments

The graph if anyone is interested - 

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v-e+f =2

v+f-1 = e + 1

Answer 1

For a Connected planar graph G,

we can write =>    V+F=E+2   (since for connected graph c=1)

so ,  8+5=E+2   => E=11. 

Answer 2

Euler's Eqn for Panar Connected Graph : 

V - E + F = 2 

Substituting we get E = 11