Annals of Combinatorics

, Volume 7, Issue 1, pp 15–20 | Cite as

Second Neighborhood via First Neighborhood in Digraphs

  • Guantao Chen
  • Jian Shen
  • Raphael Yuster
Original article

Abstract.

Let D be a simple digraph without loops or digons. For any \( v\in V(D) \), 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 \( |N^{++}(v)|\geq\gamma|N^+(v)| \), where γ = 0.657298... is the unique real root of the equation 2x3 + x2 -1 = 0.

Mathematics Subject Classification2000: 05C38¶Key words and phrases: digraph, cycle, in-degree, out-degree, neighborhood 

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Copyright information

© Birkhäuser Verlag Basel, 2003

Authors and Affiliations

  • Guantao Chen
    • 1
  • Jian Shen
    • 2
  • Raphael Yuster
    • 3
  1. 1.Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA, gchen@mathstat.gsu.eduUS
  2. 2.Department of Mathematics, Southwest Texas State University, San Marcos, TX 78666, USAUS
  3. 3.Department of Mathematics, University of Haifa-Oranim, Tivon 36006, IsraelIL

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