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
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
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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