On the Number of Perfect Star Packing and Perfect Pseudo Matching in Some Fullerene Graphs

Document Type : Research Paper


1 University of Applied Science and Technology (UAST), Tehran, IRAN

2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran


A perfect star packing in a fullerene graph G is a spanning subgraph of G whose every component is isomorphic to the star graph K_1,3. A perfect pseudo matching of a fullerene graph G is a spanning subgraph H of G such that each component of H is either K_2 or K_1,3. In this paper, we examine the number of perfect star packing in (3,6)-fullerene graphs and perfect pseudo matching in chamfered fullerene graphs.


Main Subjects

[1] H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl and R. E. Smalley, C60 Buckminsterfullerene,
Nature 318 (1985) 162–163.
[2] B. Grünbaum and T. S. Motzkin, The number of hexagons and the simplicity of geodesics
on certain polyhedra, Canadian J. Math. 15 (1963) 744–751.
[3] D. J. Klein and X. Liu, Theorems for carbon cages, J. Math. Chem. 11 (1992) 199–205,
[4] P. W. Fowler, J. E. Cremona and J. I. Steer, Systematics of bonding in non-icosahedral
carbon clusters. Theor. Chim. Acta. 73 (1988) 1–26.
[5] P. W. Fowler and D. E. Manolopoulos, An atlas of Fullerenes, Clarendon Press, Oxford,
[6] J. Petersen, Die theorie der regulären graphs, Acta Math. 15 (1891) 193–220,
[7] T. Došlic, Block allocation of a sequential resource. Ars Math. Contemp. 17 (2019) 79–88,
[8] A. Xavier, S. Theresal and S. M. J. Raja, Induced h-packing k-partition number
for certain nanotubes and chemical graphs, J. Math. Chem. 58 (2020) 1177–1196,
[9] T. Došlic, M. Taheri-Dehkordi and G. H. Fath-Tabar, Packing stars in fullerenes, J. Math.
Chem. 58 (2020) 2223–2244.
[10] T. Došlic, M. Taheri-Dehkordi and G. H. Fath-Tabar, Shortest perfect pseudo-matchings
in fullerene graphs, Appl. Math. Comput. 424 (2022) p. 127026,
[11] K. Balasubramanian, Combinatorics of edge symmetry: chiral and achiral edge colorings
of icosahedral giant fullerenes: C80, C180, and C240, Symmetry 12 (2020) p. 1308,
[12] K. Balasubramanian, O. Ori, F. Cataldo, A. R. Ashrafi and M. V. Putz, Face colorings and
chiral face colorings of icosahedral giant fullerenes: C80 to C240, Fuller. Nanotub. Carbon
Nanostruct. 29 (2021) 1–12, https ://doi.org/10.1080/15363 83X.2020.1794853.
[13] M. V. Diudea, M. Stefu, P. E. John and A. Graovac, Generalized operations on maps.
Croat. Chem. Acta. 79 (2006) 355–362.
[14] R. B. King and M. V. Diudea, The chirality of icosahedral fullerenes: a comparison of the
tripling, (leapfrog), quadrupling (chamfering) and septupling (capra) transformations, J.
Math. Chem. 39 (2006) 597–604.
[15] M. Taheri-Dehkordi and G. H. Fath-Tabar, Nice pairs of pentagons in chamfered
Fullerenes, MATCH Commun. Math. Comput. Chem. 87 (2022) 621–628,
[16] T. Došlic, All pairs of pentagons in leapfrog fullerenes are nice, Mathematics 8 (2020) P.
2135, https://doi.org/10.3390/math8122135.