Suppose G is a simple graph with n ≥ 1 vertices such that every vertex has degreeat least (n − 1)/2. Prove that G must be connected.(Hint: you may wish to prove this by induction on n) 2. Suppose G is a simple graph with n > 1 vertices such that every vertex has degreeat least (n – 1)/2. Prove that G must be connected.(Hint: you may wish to prove this by induction on n).

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Answered: Suppose G is a simple graph with n >1…

Suppose G is a simple graph with n >1 vertices such that every vertex has degree at least (n – 1)/2. Prove that G must be connected. (Hint: you may wish to prove this by induction on n).

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

Suppose G is a simple graph with n ≥ 1 vertices such that every vertex has degree
at least (n − 1)/2. Prove that G must be connected.
(Hint: you may wish to prove this by induction on n)

2. Suppose G is a simple graph with n > 1 vertices such that every vertex has degree
at least (n – 1)/2. Prove that G must be connected.
(Hint: you may wish to prove this by induction on n).

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