najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2026-17-1-17-25najo-1683Research ArticleMATHEMATICSМАТЕМАТИКАThe uniqueness of perfect star packings and the existence of pseudo-matchings in (2,6)-fullerene graphsЕдинственность идеальных звездных упаковок и существование псевдосоответствий в графах фуллеренов (2,6)https://orcid.org/0000-0002-6085-2622Тахери-ДехкордиМ.Taheri-DehkordiM.

Meysam Taheri-Dehkordi

Tehran

m.taheri@uast.ac.irUniversity of Applied Science and TechnologyIslamic Republic of Iran2026040320261711725Copyright © Taheri-Dehkordi M., 20262026Тахери-Дехкорди М.Taheri-Dehkordi M.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1683

A perfect star packing can be described as a spanning subgraph whose connected components are isomorphic to the star graph K1,3. A perfect pseudo-matching is a spanning subgraph in which every component is isomorphic to either K2 or K1,3. The study of packing problems on fullerene graphs is of particular interest due to their potential relevance in describing local bonding arrangements in carbon nanostructures. In this paper, we study the uniqueness of perfect star packing, and the existence of pseudo-matchings in (2, 6)- fullerene graphs. Moreover, we show that the perfect star packing in these graphs is unique. Furthermore, we introduced some perfect pseudo-matchings in (2, 6)-fullerene graphs.

Идеальная звездная упаковка может быть описана как остовный подграф, связные компоненты которого изоморфны звездному графу K1;3. Идеальное псевдосоответствие — это остовный подграф, в котором каждая компонента изоморфна либо K2, либо K1;3. Изучение задач упаковки на графах фуллеренов представляет особый интерес из-за их потенциальной значимости в описании локальных связей в углеродных наноструктурах. В данной работе мы изучаем уникальность идеальной звездной упаковки и существование псевдосоответствий в графах фуллеренов (2;6). Более того, мы показываем, что идеальная звездная упаковка в этих графах уникальна. Кроме того, мы ввели некоторые идеальные псевдосоответствия в графах фуллеренов (2;6).

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The authors declare that there are no conflicts of interest present.