5. (13 points) Let T' be a tree with n leaves and m non-leaf nodes. Suppose that all non-leaf nodes have degree 5. Is n = 3m + 2 always true? You must either prove the equality formally or find a counterexample.

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02-陳奕霖 Allen

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2021/09/09

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6. (13 points) A football has pentagons and hexagons on its surface (not necessarily regular). Suppose that the seams of these pentagons and hexagons form a cubic graph (a graph with every vertex having degree 3). How many pentagons does this foorball have? Prove your answer formally. (You must prove that no other values are possible.)

5. (13 points) Let T' be a tree with n leaves and m non-leaf nodes. Suppose that all non-leaf nodes have degree 5. Is n = 3m + 2 always true? You must either prove the equality formally or find a counterexample.

詳解 (共 1 筆)

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