Second Neighborhood via First Neighborhood in Digraphs
نویسندگان
چکیده
Let D be a simple digraph without loops or digons. For any v ∈ V (D), the first out-neighborhood N(v) is the set of all vertices with out-distance 1 from v and the second neighborhood N(v) of v is the set of all vertices with out-distance 2 from v. We show that every simple digraph without loops or digons contains a vertex v such that |N++(v)| ≥ γ|N+(v)|, where γ = 0.657298 . . . is the unique real root of the equation 2x + x − 1 = 0.
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