Counting largest mutual-visibility and general position sets of glued $t$-ary trees

Klavžar, Sandi (author), Lakshmanan S., Aparna (author), Roy, Dhanya (author)

All four invariants of the mutual-visibility problem and, all four invariants of the general position problem are determined for glued binary trees. The number of the corresponding extremal sets is obtained in each of the eight situations. The results are further extended to glued $t$-ary trees, and some of them also to generalized glued binary trees.

• Language: English
• Keywords: mutual-visibility set, general position set, glued binary tree, glued t-ary tree, generalized glued binary tree, enumeration
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.11.2025
• Year: 2025
• Number of pages: 14 str.
• Numbering: Vol. 80, iss. 7, art. no. 207
• PID: 20.500.12556/RUL-174514
• UDC: 519.17
• ISSN on article: 1422-6383
• DOI: 10.1007/s00025-025-02529-9
• COBISS.SI-ID: 251612931
• Publication date in RUL: 03.10.2025

Record is a part of a journal

• Title: Results in mathematics
• Shortened title: Results math.
• Publisher: Springer
• ISSN: 1422-6383
• COBISS.SI-ID: 514963225

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: množica vzajemne vidnosti, množica v splošni legi, lepljeno dvojiško drevo, lepljeno t-arno drevo, posplošeno lepleno dvojiško drevo, preštevanje