Does the graph have an Euler circuit? If the graph does not have an Euler circuit, explain why not. If it does have an Euler circuit, describe one. A graph with 10 vertices and 14 edges is shown. Vertex v0 is connected to vertex v1 and to vertex v9. Vertex v1 is connected to vertex v0, to vertex v2, to vertex v4, to vertex v5, and to vertex v8. Vertex v2 is connected to vertex v1 and to vertex v3. Vertex v3 is connected to vertex v2 and to vertex v4. Vertex v4 is connected to vertex v1 and to vertex v3. Vertex v5 is connected to vertex v1, to vertex v6, to vertex v7, and to vertex v8. Vertex v6 is connected to vertex v5 and to vertex v7. Vertex v7 is connected to vertex v5, to vertex v6, and to vertex v9. Vertex v8 is connected to vertex v1, to vertex v5, and to vertex v9. Vertex v9 is connected to vertex v0, to vertex v7, and to vertex v8. One Euler circuit is: v0 v1 v2 v3 v4 v1 v5 v6 v7 v9 v0 v1 v8 v5 v6 v7 v5 v8 v9 v0 One Euler circuit is: v0 v1 v2 v3 v4 v1 v5 v6 v7 v5 v8 v9 v0 One Euler circuit is: v0 v1 v2 v3 v4 v1 v5 v6 v7 v9 v8 v1 v0 This graph does not have an Euler circuit because vertices v1, v7, v8, and v9 have odd degree. This graph does not have an Euler circuit because vertices v0, v2, v3, v4, v5, and v6 have an even degree. This graph does not have an Euler circuit because the graph is not connected.

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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Does the graph have an Euler circuit? If the graph does not have an Euler circuit, explain why not. If it does have an Euler circuit, describe one.

A graph with 10 vertices and 14 edges is shown.

Vertex v₀ is connected to vertex v₁ and to vertex v₉.
Vertex v₁ is connected to vertex v₀, to vertex v₂, to vertex v₄, to vertex v₅, and to vertex v₈.
Vertex v₂ is connected to vertex v₁ and to vertex v₃.
Vertex v₃ is connected to vertex v₂ and to vertex v₄.
Vertex v₄ is connected to vertex v₁ and to vertex v₃.
Vertex v₅ is connected to vertex v₁, to vertex v₆, to vertex v₇, and to vertex v₈.
Vertex v₆ is connected to vertex v₅ and to vertex v₇.
Vertex v₇ is connected to vertex v₅, to vertex v₆, and to vertex v₉.
Vertex v₈ is connected to vertex v₁, to vertex v₅, and to vertex v₉.
Vertex v₉ is connected to vertex v₀, to vertex v₇, and to vertex v₈.

One Euler circuit is: v₀ v₁ v₂ v₃ v₄ v₁ v₅ v₆ v₇ v₉ v₀ v₁ v₈ v₅ v₆ v₇ v₅ v₈ v₉ v₀ One Euler circuit is: v₀ v₁ v₂ v₃ v₄ v₁ v₅ v₆ v₇ v₅ v₈ v₉ v₀ One Euler circuit is: v₀ v₁ v₂ v₃ v₄ v₁ v₅ v₆ v₇ v₉ v₈ v₁ v₀ This graph does not have an Euler circuit because vertices v₁, v₇, v₈, and v₉ have odd degree. This graph does not have an Euler circuit because vertices v₀, v₂, v₃, v₄, v₅, and v₆ have an even degree. This graph does not have an Euler circuit because the graph is not connected.

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