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Characterization of Trees with Maximum Security

  • Alex Alochukwu
    ,
  • Audace Dossou-Olory
    ,
  • Fadekemi Janet Osaye
    ,
  • Valisoa R.M. Rakotonarivo
    ,
  • Shashank Ravichandran
    ,
  • Sarah J. Selkirk
  • Albany State University
    ,
  • Université d’Abomey-Calavi
    ,
  • Troy University
    ,
  • University of Pretoria
    ,
  • University of Deleware
    ,
  • University of Klagenfurt
Research Output: Contribution to journal Article Peer-review

Open access

Abstract

The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the sum of ranks over all vertices (known as the security) in proper binary trees, and produce a classification of families of proper binary trees for which the security is maximized. In addition, extremal results relating to the maximum rank among all vertices in families of trees are discussed

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