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Let G = (V, E) be a graph and let u and v be vertices. Assume that there is a walk v1, e1, V2,...,Vn-1, en-1, Vn such that V₁ = u and V₁ = v and assume that amongst all such walks this one has been chosen so that n is as small as possible. Explain why the walk contains no repeated vertices.

Let G = (V, E) be a graph and let u and v be vertices. Assume that there is a walk v1, e1, V2,...,Vn-1, en-1, Vn such that V₁ = u and V₁ = v and assume that amongst all such walks this one has been chosen so that n is as small as possible. Explain why the walk contains no repeated vertices.

Advanced Engineering Mathematics
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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Let G = (V, E) be a graph and let u and v be vertices. Assume that there is a walk V1, C1, V2, ...,Vn-1, en-1, Vn such that v₁ = u and V₂ = v and assume that amongst all such walks this one has been chosen so that n is as small as possible. Explain why the walk contains no repeated vertices.
Transcribed Image Text:Let G = (V, E) be a graph and let u and v be vertices. Assume that there is a walk V1, C1, V2, ...,Vn-1, en-1, Vn such that v₁ = u and V₂ = v and assume that amongst all such walks this one has been chosen so that n is as small as possible. Explain why the walk contains no repeated vertices.
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