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