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+5 votes
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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. $13$
asked in Graph Theory by Boss (18.3k points)
edited by | 925 views
0
Why is it marked out of syllabus?Is graph theory is not in syllabus?
0
its in

2 Answers

+12 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
answered by Boss (14.4k points)
edited by
0
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.
0 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
answered ago by Active (4.4k points)
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