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Projective dimension of closed neighborhood hypergraphs via extended double covers
Let $G$ be a finite and simple graph without isolated vertices. We investigate the projective dimension of the closed neighborhood hypergraph $\mathcal{N}[G]$ and its relationship with the Castelnuovo-Mumford regularity of the extended bipartite double cover $\mathfrak{B}_e(G)$ of $G$. We establish
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