Year: 2007
Type: preprint
Abstract: 1 For a simple graph G let NG[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 NG[u] ⊆ NG[v]; and a graph H is closed-neighborhood distinct (CND) if every closed-neighborhood is distinct, i.e., if NH [u] 6 = NH [v] when u 6 = v, for all u and v ∈ V (H). In this paper we are mainly concerned with constructing CNAS graphs. We construct a family of connected CNAS graphs with n vertices for each fixed n ≥ 2. We list all connected CNAS graphs with ≤ 6 vertices, and find the smallest connected CNAS graph that lies outside these families. We indicate how some CNAS graphs can be constructed from a related type of graph, called a NAS graph. Finally, we present an algorithm to construct all CNAS graphs on a
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W212189368