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arXiv 2018-01-25 2 views

Existence of connected regular and nearly regular graphs

Ganesan, Ghurumuruhan

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For integers k ≥ 2 and n ≥ k+1, we prove the following: If n· k is even, there is a connected k-regular graph on n vertices. If n· k is odd, there is a connected nearly k-regular graph on n vertices.

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