Characterization of Trees with Maximum Security
Combinatorics
2026-04-15 v5
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 binary trees, and produce a classification of families of binary trees for which the security is maximized. In addition, extremal results relating to maximum rank among all vertices in families of trees is discussed.
Keywords
Cite
@article{arxiv.2411.19188,
title = {Characterization of Trees with Maximum Security},
author = {Alex S. A. Alochukwu and Audace A. V. Dossou-Olory and Fadekemi J. Osaye and Valisoa R. M. Rakotonarivo and Shashank Ravichandran and Sarah J. Selkirk and Hua Wang and Hays Whitlatch},
journal= {arXiv preprint arXiv:2411.19188},
year = {2026}
}
Comments
This work is an output of the American Mathematical Society's Mathematics Research Community (MRC): Trees in Many Contexts