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Second Neighborhood via First Neighborhood in Digraphs
G. Chen1, J. Shen2, and R. Yuster3
1Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA
2Department of Mathematics, Southwest Texas State University, San Marcos, TX 78666, USA
3Department of Mathematics, University of Haifa-Oranim, Tivon 36006, Israel
Annals of Combinatorics 7 (1) p.15-20 March, 2003
AMS Subject Classification: 05C38
Let D be a simple digraph without loops or digons. For any , the first out-neighborhood is the set of all vertices with out-distance 1 from v and the second neighborhood 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 , where is the unique real root of the equation .
Keywords: digraph, cycle, in-degree, out-degree, neighborhood


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