Let G be a simple graph with exactly 11 vertices. Prove that G or its complement G must be non-planar. Hint: The maximum number of edges in a planar graph with n vertices is 3n − 6. Please write in complete sentences, include all details, show all of your work, and clarify all of your reasoning.

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Let G be a simple graph with exactly 11 vertices. Prove that G or its complement G must be
non-planar. Hint: The maximum number of edges in a planar graph with n vertices is 3n − 6.
Please write in complete sentences, include all details, show
all of your work, and clarify all of your reasoning.

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