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.
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