Answered: 5. Prove Corollary 3.6: "Let u and v be…

5. Prove Corollary 3.6: "Let u and v be vertices of a 2-connected graph G. Then there is a cycle of G that contains both u and v.” (Hint: you may use Theorem 3.5.)

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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Theorem 3.5 states the following:

Let G be a loopless graph with at least three vertices, and no isolated vertices. Then G is 2-connected if and only if, for every pair {e, f} of edges of G, there is a cycle of G that contains both e and f.

5. Prove Corollary 3.6: "Let u and v be vertices of a 2-connected graph G. Then
there is a cycle of G that contains both u and v.” (Hint: you may use Theorem 3.5.)

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