1. Let F be a forest with n vertices and k connected components, with 1 ≤ k ≤ n.(a) Compute Xv∈V (F)deg(v) in terms of n and k.(b) Show that the average degree of a vertex in F is strictly less than 2.(c) Conclude that forests have leaves. 1. Let F be a forest with n vertices and k connected components, with 1 deg(v) in terms of n and k.veV (F)(b) Show that the average degree of a vertex in F is strictly less than 2.(c) Conclude that forests have leaves.

Answered: Image /qna-images/answer/5c130d69-e73a-4700-b474-69d767b2b15d.jpg

. Let F be a forest with n vertices and k connected components, with 1 deg(v) in terms of n and k. vEV(F) (b) Show that the average degree of a vertex in F is strictly less than 2. (c) Conclude that forests have leaves.

. Let F be a forest with n vertices and k connected components, with 1 deg(v) in terms of n and k. vEV(F) (b) Show that the average degree of a vertex in F is strictly less than 2. (c) Conclude that forests have 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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Question

1. Let F be a forest with n vertices and k connected components, with 1 ≤ k ≤ n.
(a) Compute X
v∈V (F)
deg(v) in terms of n and k.
(b) Show that the average degree of a vertex in F is strictly less than 2.
(c) Conclude that forests have leaves.

1. Let F be a forest with n vertices and k connected components, with 1<k < n.
(a) Compute> deg(v) in terms of n and k.
veV (F)
(b) Show that the average degree of a vertex in F is strictly less than 2.
(c) Conclude that forests have leaves.

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