Math, asked by rishabbagga96, 10 months ago

A connected graph has 9 vertices having degrees 2, 2, 2, 3, 3, 3, 4, 4 and 5.
How may edges are there ? How many faces are there ?

Answers

Answered by amitnrw
6

14 Edges  & 7 Faces if A connected graph has 9 vertices having degrees 2, 2, 2, 3, 3, 3, 4, 4 and 5.

Step-by-step explanation:

A connected graph has 9 vertices having degrees 2, 2, 2, 3, 3, 3, 4, 4 and 5.

Number of Edges  = (2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 5)/2

= 28/2

= 14

14 Edges are there

Euler formula for faces

= Edges - Vertex + 2

= 14 - 9 + 2

= 7

7 Faces are there

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Answered by itzheartcracker13
20

As there are 7 entries in degree sequence so ,

No of vertices = 7

Now applying Handshaking Theorem , we have

Sum of degrees = 2 * No of edges

==> 2 e = 3 * 6 + 6

==> e = 24 / 2 = 12

Now assuming the planarity and assuming only one connected component and hence applying Euler's formula we have :

No of faces = e - n + 2

= 12 - 7 + 2

= 7

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