A tree has 7 vertices.   (i)  How many edges this tree can have?    (ii) If the degrees of first six vertices are  1,1,1,2,2 and 3 then what is the degree of         next vertex? Show all your work.    (iii) If the degrees of vertices are 1,1,2,2,3,3 and 4 then is it possible to have such           tree? Explain with detail

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CR: Chapter Review
Problem 71E
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A tree has 7 vertices.

  (i)  How many edges this tree can have? 

  (ii) If the degrees of first six vertices are  1,1,1,2,2 and 3 then what is the degree of 

       next vertex? Show all your work.

   (iii) If the degrees of vertices are 1,1,2,2,3,3 and 4 then is it possible to have such 

         tree? Explain with detail.

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