najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1597Research ArticleMATHEMATICSМАТЕМАТИКАThe Uniqueness of Perfect Star Packings and the Existence of Pseudo-Matchings in (2,6)-Fullerene Graphshttps://orcid.org/0000-0002-6085-2622Taheri-DehkordiMeysamm.taheri@uast.ac.irUniversity of Applied Science and Technology, Tehran, IranRussian Federation2026050320261711597Copyright © Taheri-Dehkordi M., 20262026Taheri-Dehkordi M.Taheri-Dehkordi M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1597

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 starpacking in these graphs is unique. Furthermore, we introduced some perfect pseudo-matchings in (2; 6)-fullerene graphs.

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