GATE | Gate IT 2008 | Question 74

A binary tree with n > 1 nodes has n₁, n₂ and n₃ nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.

Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?
(A) 2 * n₁ – 3
(B) n₂ + 2 * n₁ – 2
(C) n₃ – n₂
(D) n₂ + n₁ – 2


Answer: (A)

Explanation: With reference to figure of answer of previous question:


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