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Bee_see

  • one year ago

Recall that we showed in class that if T is a tree with least 2 vertices, then T contains a leaf. (A leaf is a vertex of degree one.) Recall also that if T is a tree with leaf x, then T − x is also a tree. (Here, T − x denotes the tree obtained by deleting x and the edge incident to x from T .) Prove by induction that if T is a tree, then the number of edges of T is one less than the number of vertices of T . (Hint: To start, let P(n) be the proposition that every tree with n vertices has n − 1 edges.)

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  1. thomas5267
    • one year ago
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    What is the definition of tree? If the definition of the tree is chosen to be a connected graph with n vertices and n-1 edges, then the proof is trivial. If the definition of the tree is chosen to be a connected graph with no cycles, then the proof is slightly more complicated.

  2. Bee_see
    • one year ago
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    what do you mean? is the function p(n)=n-1?

  3. thomas5267
    • one year ago
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    What definition of tree would you like to use?

  4. Bee_see
    • one year ago
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    It's fine. I was able to solve the problem.

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