New Expansion for Certain Isomers of Various Classes of Fullerenes

Document Type : Original Scientific Paper


1 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran

2 School of Mathematics, Iran University of Science and Technology, P.O.Box 16846-13114, Tehran, Iran


This paper is dedicated to propose an algorithm in order to generate the certain isomers of some well-known fullerene bases. Furthermore, we enlist the bipartite edge frustration correlated with some of symmetrically distinct infinite families of fullerenes generated by the offered process.


Main Subjects

1. Y. Alizadeh, V. Andova, S. Klavžar, R. Škrekovski, Wiener dimension: fundamental properties and (5;0)-nanotubical fullerenes, MATCH Commun. Math. Comput. Chem. 72 (2014) 279–294.
2. V. Andova, T. Došlić, M. Krnc, B. Lužar, R. Škrekovski, On the diameter and some related invariants of fullerene graphs, MATCH Commun. Math. Comput. Chem. 68 (2012) 109–130.
3. V. Andova, F. Kardoš, R. Škrekovski, Sandwiching saturation number of fullerene graphs, MATCH Commun. Math. Comput. Chem. 73 (2015) 501–518.
4. V. Andova, F. Kardoš, R. Škrekovski, Mathematical aspects of fullerenes, Ars Math. Contemp. 11 (2016) 353–379.
5. G. Brinkmann, A. W. M. Dress, A constructive enumeration of fullerenes, J. Algorithams 23 (1997) 345–358.
6. G. Brinkmann, J. Goedgebeur, B. D. McKay, The generation of fullerenes, J. Chem. Inf. Model. 52 (2012) 2910–2918.
7. T. Došlić, On some structural properties of fullerene graphs, J. Math. Chem. 31 (2002) 187–195.
8. T. Došlić, T. Rèti, Spectral properties of fullerene graphs, MATCH Commun. Math. Comput. Chem. 66 (2011) 733–742.
9. T. Došlić, D. Vukičević, Computing the bipartite edge frustration of fullerene graphs, Discrete Appl. Math. 155 (2007) 1294–1301.
10. T. Došlić, The smallest eigenvalue of fullerene graphs - closing the gap, MATCH Commun. Math. Comput. Chem. 70 (2013) 73–78.
11. M. Endo, H. W. Kroto, Formation of carbon nanofibers, J. Phys. Chem. 96 (1992) 6941–6944.
12. P. W. Fowler, S. Daugherty, W. Myrvold, Independence number and fullerene stability, Chem. Phys. Lett. 448 (2007) 75–82.
13. P. W. Fowler, D. E. Manolopoulos, D. B. Redmond, R. P. Ryan, Possible symmetries of fullerene stuctures, Chem. Phys. Lett. 202 (1993) 371–378.
14. P. W. Fowler, D. B. Redmond, Symmetry aspects of bonding in carbon clusters: the leapfrog transformation, Theor. Chim. Acta 83 (1992) 367–375.
15. H. Hua, M. Faghani, A. R. Ashrafi, The Wiener and Wiener polarity indices of a class of fullerenes with exactly 12n carbon atoms, MATCH Commun. Math. Comput. Chem. 71 (2014) 361–372.
16. D. E. Manolopoulos, J. C. May, S. E. Down, Theoretical studies of the fullerenes: C34 to C70, Chem. Phys. Lett. 181 (1991) 105–111.
17. D. E. Manolopoulos, P. W. Fowler, A fullerene without a spiral, Chem. Phys. Lett. 204 (1993) 1–7.
18. A. J. Stone, D. J. Wales, Theoretical studies of icosahedral C60 and some related species, Chem. Phys. Lett. 128 (1986) 501–503.