in Graph Theory edited by
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16 votes
16 votes

Let $G$ be a simple connected planar graph with $13$ vertices and $19$ edges. Then, the number of faces in the planar embedding of the graph is:

  1. $6$
  2. $8$
  3. $9$
  4. $13$
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Why is it marked out of syllabus?Is graph theory is not in syllabus?
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its in
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3 Answers

22 votes
22 votes
Best answer
$f=e-n+2$ where $f$ denotes number of faces E the number of edges $n$ the number of vertices So $f=19-13+2 = 8$ faces

Correct Answer: $B$
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2 Comments

Being simple graph cant we use the formula 3*R<=2*E if we use this then answer turns out to be 13.Please tell me what is wrong in my logic.
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For k components,

e – n + (k+1) = f

For connected, k=1

e-n+2=f
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4 votes
4 votes
f=e-n+(k+1)

f=number of faces,

e=number of edges,

n=number of vertices,

k=number of connected components,

for connected graph k=1,so

f=e-n+(1+1)

f=e-n+2

f=19-13+2

f=8
1 vote
1 vote
Answer will be (b) 8 because

f+v-e = 2 for connected graph

f = 2+6 = 8  

f is the no. of regions or faces

e is the number of edges

v is the number of vertices
Answer: