Almost all trees are decay-unstable

Rupnik Poklukar, Darja (author), Žerovnik, Janez (author)

Decay centrality is a centrality measure that was introduced to address the sensitivity of traditional closeness measures to distant vertices. We prove that almost all trees are not decay stable, confirming a conjecture of Coroničova Hurajová, Gago and Madaras (2018). A construction that generates all decay stable trees is also given.

• Language: English
• Keywords: centrality measure, decay stability, trees
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 16 str.
• Numbering: Vol. 132, no. 1
• PID: 20.500.12556/RUL-185570
• UDC: 519.172.1
• ISSN on article: 0025-5521
• DOI: 10.2140/mscand.2026.132.1
• COBISS.SI-ID: 287350787
• Publication date in RUL: 10.08.2026

Record is a part of a journal

• Title: Mathematica Scandinavica
• Shortened title: Math. Scand.
• Publisher: Dansk Matematisk Forening, áIslenzka StærŸræëfélagiú, Norsk matematisk forening, Suomen Matemaattinen Yndistys-Finlands Matematiska Förening, Svenska Matematikersamfundet
• ISSN: 0025-5521
• COBISS.SI-ID: 25910272

Secondary language

• Language: Slovenian
• Keywords: mere centralnosti, razpadna stabilnost, drevesa