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The regularity of the Rees ring of the edge ideal of a finite simple graph isstudied. We show that the matching number is a lower and matching number~$+1$is an upper bound of the regularity, if the Rees algebra is normal. In generalthe induced matching number is a lower bound for the regularity, which can beshown by applying the squarefree divisor complex.

Matching numbers and the regularity of the Rees algebra of an edge ideal