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Closed-Neighborhood Anti-Sperner Graphs, John P. Mcsorley, Alison Marr, Thomas D. Porter, Walter D. Wallis

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For a simple graph G let N_G[u] denote the closed-neighborhood of vertex u ∈ V (G). Then G is closed-neighborhood anti-Sperner (CNAS) if for every u there is a v ∈ V (G)\{u} with N_G [u] ⊆ N_G [v] and a graph H is closed-neighborhood distinct (CND) if every closed-neighborhood is distinct, i.e., if N_H[u] ≠ N_H[v] when u ≠ v, for all u and v ∈ V (H).

In this paper we …