Official PYQ · 2021Set 1 · Q16Graphs: Connectivity, Matching, ColouringNAT1 mark

GATE CS 2021 Set 1 Q16 — Graphs: Connectivity, Matching, Colouring

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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Answer: 11 : 11

According to Euler's formula for any connected planar graph:

V - E + F = 2

where:

$V$ is the number of vertices
$E$ is the number of edges
$F$ is the number of faces (including the outer unbounded face)

Given in the problem:

Number of vertices, $V = 8$
Number of faces, $F = 5$

Substituting these values into Euler's formula:

8 - E + 5 = 2

13 - E = 2

E = 11

Thus, the number of edges in $G$ is 11.

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Published 10 Oct 2026

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