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Prove that in a full binary tree with n vertices, the number of pendant vertices is (n+1)/2.
written 7.8 years ago by gravatar for teamques10 teamques10 ★ 67k modified 2.7 years ago by gravatar for sagarkolekar sagarkolekar ★ 11k
discrete mathematics
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written 7.8 years ago by gravatar for teamques10 teamques10 ★ 67k modified 2.4 years ago by gravatar for yogeshtalp524 yogeshtalp524 • 30

In a full binary tree, only one vertex, namely, the root is of even degree (namely 2) and each of the other (n-1) vertices is of odd degree (namely 1 or 3.)

Since the number of vertices of odd degree in an undirected graph is given even, (n-1) is even. …

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