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CMI2015-A-05

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An undirected graph has $10$ vertices labelled $1, 2,\dots , 10$ and $37$ edges. Vertices $1, 3, 5, 7, 9$ have degree $8$ and vertices $2, 4, 6, 8$ have degree $7.$ What is the degree of vertex $10$ ?

  1. $5$
  2. $6$ 
  3. $7$ 
  4. $8$

2 Answers

Best answer
15 15 votes

Vertices $1, 3, 5,7,9$ have degree $8$ and vertices $2, 4, 6, 8$ have degree $7$.

We know tht in a graph Sum of degrees $= 2\times \text{No. of edges}$
 
Let $X =$ degree of vertex $10$

$8 + 7 + 8 + 7 + 8 + 7 + 8 + 7 + 8 + X =  2\times 37$

$68 + X =74$

$X=6$

Hence,Degree of vertex $10$ is $6$.

Hence, Option (B) $6$ is the correct choice.

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Answer: (b) 6

The sum of the degrees is twice the number of edges, which is 74 in this case. The degrees of the vertices {1, 2, . . . , 9} add up to 68. Hence 6 is the correct answer.

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