Prove that every non-leaf in a tree is a cut-vertex. (Recall a cut-vertex is a vertex whose removal will disconnect the graph). Hint: Show two neighbors of the non-leaf x are in different components of T - X.

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24-06-2024
Mathematics

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Prove that every non-leaf in a tree is a cut-vertex. (Recall a cut-vertex is a vertex whose removal will disconnect the graph). Hint: Show two neighbors of the non-leaf x are in different components of T - X.

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