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    Proofs: K-Regular Graphs

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    Prove that
    1) If n and k are odd positive integers with k<=n-1, then there are no graphs G such that G is k-regular with order n.
    2) If n is even, k is a positive integer such that k<=n-1, then there are k-regular graphs with order n.

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    Solution Preview

    1) By contradiction. If G is a k-regular graph with order n, then the sum of ...

    Solution Summary

    Statements involving k-regular graphs are proven.The positive integer and functions are examined.