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

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GATE CS 2021 Official Paper: Shift 1
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Data

Number of vertices = V = 8

Number of faces = 5

Number of edges = E

Euler's formula:

V + F = E + 2

Calculation

⇒ E = V + F - 2

⇒ E = 8 + 5 - 2

⇒ E = 11 

∴ Number of edges is 11

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