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In this paper, we first give some sufficient criteria for normality ofmonomial ideals. As applications, we show that closed neighborhood ideals ofcomplete bipartite graphs are normal, and hence satisfy the (strong)persistence property. We also prove that dominating ideals of completebipartite graphs are nearly normally torsion-free. In addition, we show thatdominating ideals of $h$-wheel graphs, under certain condition, are normal.

Normality and associated primes of Closed neighborhood ideals and dominating ideals