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Let $G$ be a simple undirected planar graph on $10$ vertices with $15$ edges. If $G$ is a connected graph, then the number of bounded faces in any embedding of $G$ on the plane is equal to

(A) 3
(B) 4
(C) 5
(D) 6

asked in Graph Theory by Boss (17.8k points)
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0
Does bounded faces mean cycles?

2 Answers

+21 votes
Best answer

For any planar graph,
$\text{n(no. of vertices) - e(no. of edges) + f(no. of faces) = 2}$

$f = 15 - 10 + 2= 7$
number of bounded faces $= \text{no. of faces -1}$
                                               $= 7 -1=6$
So, the correct answer would be D

answered by Active (2.6k points)
edited by
0

"number of bounded faces = no. of faces -1" is this formula ?

+3

number of bounded faces = no. of faces -1 (​external or unbounded face)

0 votes
Number of edges in minimally connected graph: n-1

So, 10-1=9 (edges used to connect all vertices)

Remaining 15-9=6 edges can be used to connect any two vertices and form a bounded face.

So ans - (d) 6

Is this analogy correct?
answered by (19 points)


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