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Manipal MET2017MathematicsStraight Lines

In a tree on a vertices there is exactly one vertex with degree 2 and remaining vertices are of degree either 1 or 3 . Then the number of pendant vertices is

Options

  1. A8
  2. B5
  3. C4
  4. D6

Correct answer

B. 5

Step-by-step solution

Total degree =2(n-1)=2 n-2 Let p be the number of pendant vertices. Then (n-p-1) are vertices with degree 3, one vertex of degree 2 . Total degree =2+p+3(n-p-1) 2 n-2=-1-2 p+3 n p= n+1 2 = 9+1 2 ( n=9 given) =5

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