8. Answer these two questions: (a) Let G = (V,E) be a loop-free connected graph with |V| ≥ 11. Prove that either G or itscomplement G must be nonplanar.(b) The result in part (a) is actually true for |V| ≥ 9, but the proof for |V|harder. Find a counterexample to part (a) for |V| = 8.= 9, 10 is much

Step 1: Understand the properties of planar and non-planar graphsPlanar graphs are graphs that can…

Answered: (a) Let G = (V,E) be a loop-free…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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(a) Let G = (V,E) be a loop-free connected graph with |V| ≥ 11. Prove that either G or its complement G must be nonplanar. (b) The result in part (a) is actually true for |V| ≥ 9, but the proof for |V| harder. Find a counterexample to part (a) for |V| = 8. = 9, 10 is much