The uniqueness of perfect star packings and the existence of pseudo-matchings in (2,6)-fullerene graphs
https://doi.org/10.17586/2220-8054-2026-17-1-17-25
Abstract
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.
About the Author
M. Taheri-Dehkordi
University of Applied Science and Technology
Islamic Republic of Iran
Islamic Republic of Iran
Meysam Taheri-Dehkordi
Tehran
References
1. Taylor P.F. In Kirk-Othmer Encyclopedia of Chemical Technology, John Wiley & Sons, Inc (Ed.), 2002.
2. Postnov V.N., Scaletckaya A.Ya., Krokhina O.A., Keskinov V.A., Charykov N.A., Semenov K.N. Sorption and liquid chromatographic separation of light fullerenes C60 and C70 with multiwall carbon nanotubes, Nanosystems: Physics, Chemistry, Mathematics, 2013, 4(5), P. 706–715.
3. Doˇsli´c T. Cyclical edge-connectivity of fullerene graphs and (k, 6)-cages, J. Math. Chem., 2003, 33, P. 103–112.
4. Doˇsli´c T., Taheri-Dehkordi M., Fath-Tabar G.H. Packing stars in fullerenes, J. Math. Chem., 2020, 58, P. 2223–2244.
5. Schwerdtfeger P., Wirz L.N., Avery J. The topology of fullerenes, WIREs Comput. Mol. Sci., 2015, 5, P. 96–145.
6. Doˇsli´c T., Taheri-Dehkordi M., Fath-Tabar G.H. Shortest perfect pseudomatchings in fullerene graphs, Appl. Math. Comput., 2022, 424, P. 127026.
7. Lingjuan Sh. The fullerene graphs with a perfect star packing, Ars Mathematica Contemporanea, 2023.
8. Taheri-Dehkordi M., Fath-Tabar G.H. Nice Pairs of Pentagons in Chamfered Fullerenes, MATCH Commun. Math. Comput. Chem., 2022, 87, P. 621–628.
9. Doˇsli´c T. On some structural properties of fullerene graphs, J. Math. Chem., 2002, 31, P. 187–195.
10. Fowler P.W., Cremona J.E., Steer J.I. Systematics of bonding in non-icosahedral carbon clusters, Theor. Chim. Acta., 1988, 73, P. 1–26.
11. Fowler P.W., Manolopoulos D.E. An Atlas of Fullerenes. International Series of Monographs on Chemistry, 30 (Clarendon Press, Oxford, 1995).
12. Shiu W.C., Zhang H. A complete characterization for k-resonant Klein-bottle polyhexes, J. Math. Chem., 2008, 43(1), P. 45–59.
13. Taheri-Dehkordi M. Introducing Two Transformations in Fullerene Graphs, Star and Semi-Star, Iranian J. Math. Chem., 2023, 14, P. 135–143.
14. Zhang F., Wang L. k-Resonance of open-ended carbon nanotubes, J. Math. Chem., 2004, 35(2), P. 87–103.
15. Taheri-Dehkordi M., Fath-Tabar G.H. On the Number of Perfect Star Packing and Perfect Pseudo Matching in Some Fullerene Graphs, Iranian J. Math. Chem., 2023, 14, P. 7–18.
16. Yang R., Yuan M. The Structural Properties of (2, 6)-Fullerenes, Symmetry, 2023, 15 (11), P. 2078.
17. Taheri-Dehkordi M. Perfect star packings in (2,6)-fullerene graphs, Math. Interdisc. Res., In press, 10.22052/mir.2025.257713.1546, 2025.
Review
For citations:
Taheri-Dehkordi M. The uniqueness of perfect star packings and the existence of pseudo-matchings in (2,6)-fullerene graphs. Nanosystems: Physics, Chemistry, Mathematics. 2026;17(1):17-25. https://doi.org/10.17586/2220-8054-2026-17-1-17-25
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