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证明:在6个结点12条边的连通平面简单图中,每个面的面度都是3。

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正确答案:

证:n=6,m=12欧拉公式n-m+f=2知f=2-n+m=2-6-12=8。由图论基本定理知:

1

所以必有2,即每个面用3条边围成。

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若图G中恰有两个奇数顶点,则这两个顶点是连通的。

证明:在6个结点12条边的连通平面简单图中,每个面的面度都是3。

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