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find the number of regions in a connected simple graph with 20 vertices each with a degree of 3 ?

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given ,

20 vertices

degree of each vertex = 3

By using Handshake lemma

20*3 = 2*E

= > E = 30

Now , using Eulers Formula ,

n - e+ f = 2

20 - 30 + f = 2

 f = 12

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