Characterization of Trees with Maximum Security
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. This work is an output of the American Mathematical Society's Mathematics Research Community (MRC): Trees in Many Contexts
Fields of Study & Subjects
Graph theory and applications
Graph Labeling and Dimension Problems
Graph Theory and Algorithms
Publication details
- Journal / source
- Discrete Mathematics & Theoretical Computer Science
- Volume
- vol. 28:2
- Issue
- Graph Theory
- Publication date
- 9 April 2026
- Language
- EN