Planar graph

Question

In a connected 3 regular graph, every planar region is bounded by exactly 5 edges, then count no of edges?

Comments

30.

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i am not sure about the answer. Please explain the procedure

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acc to handshaking lemma ,

sum of all degree = 2  *|E|

given , 3-regular graph

3 V = 2|E|

V = 2 E / 3

 

every planar region is bounded by exactly 5 edges

assume , there is F --- > faces

for a planar graph with vertices

sum of degree (faces) = 2*E

5 F = 2 E

F = 2E / 5

 

now put the V and F in

V -E + F =  2

and got E = 30 edges

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the same approach as Magma explained.

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Thanks.

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One Doubt though.. Degree of region= The number of edges that bounds the region right ?

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Yes.