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What is the number of vertices in an undirected connected graph with $27$ edges, $6$ vertices of degree $2, 3$ vertices of degree $4$ and remaining of degree $3$?

  1. $10$
  2. $11$
  3. $18$
  4. $19$
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2 Answers

Best answer
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39 votes

sum of degree of all the vertices $= 2 *$ number of edges.

$2\times 6 + 4\times 3 + 3\times x = 27\times 2$

$x=10.$

Number of vertices $= 6 + 3 +x = 19.$

The correct answer is (D).

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