Answered: 3. (Exercise 3.4) Prove Lemma 3.3: "Let…

3. (Exercise 3.4) Prove Lemma 3.3: "Let G be a 2-connected graph. If e and f are parallel edges in G, then G\e is 2-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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Question

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I have to prove the following lemma: “Let G be a 2-connected graph. If e and f are parallel edges in G, then G\e is 2-connected.”

I was thinking about proving it by showing that there exists a cycle betweent two adjacent vertices u and v such that if we were to delet one of the edges, either e or f, we would remain in a 2-connected graph. I'm not sure if this is correct and even how to word it properly. Please help me with this prove, thank you :)

3. (Exercise 3.4) Prove Lemma 3.3: "Let G be a 2-connected graph. If e and f are
parallel edges in G, then G\e is 2-connected."

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