The completeness number of neighborhood graphs
نویسندگان
چکیده
Let G = (V,E) be a simple undirected graph. N(G) = (V,EN ) is the neighborhood graph of G, if and only if EN = {{a, b} ∣ a ∕= b ∧ ∃x ∈ V : {x, a} ∈ E ∧ {x, b} ∈ E}. It is well-known that the neighborhood graph N(G) is connected if and only if the graph G is connected and non-bipartite. We present some results concerning the k-iterated neighborhood graph Nk(G) := N(N(. . . N(G))) of G. So we determine which types of graphs occur as k-iterated neighborhood graphs Nk(G) for large k; further we investigate conditions for G and k such that Nk(G) becomes a complete graph.
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