# 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.

https://brainmass.com/math/graphs-and-functions/proofs-regular-graphs-7032

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Proof

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.

$2.49