Work

Characterization of Trees with Maximum Security

Year: 2026

Type: article

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

Source: Discrete Mathematics & Theoretical Computer Science

DOI: 10.46298/dmtcs.14872

Authors: Alex S. A. Alochukwu, Audace A. V. Dossou-Olory, Fadekemi J. Osaye, Valisoa R. M. Rakotonarivo, Shashank Ravichandran, Sarah J. Selkirk, Hua Wang, Hays Whitlatch

Institutions: Albany State University, Université d'Abomey-Calavi, Institute of Mathematics and Physics, Troy University, University of Pretoria, University of Delaware, University of Klagenfurt, University of Warwick, Georgia Southern University, Gonzaga University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Austrian Science Fund, Engineering and Physical Sciences Research Council

Awards: Mathematics Research Communities, Modeling–Analysis–Optimization of discrete, continuous, and stochastic systems, G4965749342, Two-way automata: limitations and frontiers

OpenAlex ID: W4405030173

FWCI:

Cites: 1

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Related to: 10