Answered: A leaf in a tree T is a vertex x E V(T)…

A leaf in a tree T is a vertex x E V(T) of degree 1. (a) Show that every finite tree T has at least A(T) leaves. (b) Deduce that every finite tree T with |V(T)| >= 2 has at least two leaves.

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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A leaf in a tree T is a vertex x E V(T) of degree 1.
(a) Show that every finite tree T has at least A(T) leaves.
(b) Deduce that every finite tree T with |V(T)| >= 2 has at least two leaves.

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