Let T be any full binary tree. A vertex v of T is called a child of a vertex u of T if there is a branch from u to v. A vertex of T is a leaf if it has no children. Vertices that have children are called internal vertices. The root of T is an internal vertex unless it is the only vertex of T in which case it is a leaf. Let L(T) denote the set of leaves of T and I(T) denote the set of internal vertices of T. Recall n(T) denotes the number of vertices of T. Use structural induction to prove that n(T) = 2L(T) – 1

Let T be any full binary tree. A vertex v of T is called a child of a vertex u of T if there is a branch from u to v. A vertex of T is a leaf if it has no children. Vertices that have children are called internal vertices. The root of T is an internal vertex unless it is the only vertex of T in which case it is a leaf. Let L(T) denote the set of leaves of T and I(T) denote the set of internal vertices of T. Recall n(T) denotes the number of vertices of T. Use structural induction to prove that n(T) = 2L(T) – 1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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