On the energy of fullerene graphs

Document Type: Original Article

Authors

Srtt University

Abstract

The concept of energy of graph is defined as the sum of the absolute values of the eigenvalues of a graph. Let λ1, λ2, . . . , λbe eigenvalues of graph G, then the energy of G is defined as E (G) =∑nn=1ه|. The aim of this paper is to compute the eigenvalues of two fullerene graphs C60 and C80.

Graphical Abstract

On the energy of fullerene graphs

Keywords


[1] A. R. Ashrafi, M. Ghorbani and M. Jalali, The vertex PI and Szeged indices of an infinite family offullerenes, J. Theor. Comput. Chem. 7 (2008) 221–231.
[2] A. R. Ashrafi, M. Jalali, M. Ghorbani and M. V. Diudea, Computing PI and Omega polynomials of an infinite family of fullerenes, MATCH Commun. Math. Comput. Chem. 60 (2008) 905–916.
[3] N. Biggs, Algebraic Graph Theory, Cambridge Univ. Press, Cambridge, 1974.
[4] D. Cvetkovi´ c, M. Doob and H. Sachs, Spectra of Graphs–Theory and Applications, Barth, Heidel-berg, 1995.
[5] D. Cvetkovi´ c, P. Rowlinson, P. Fowler, D. Stevanovi ´ c, Constructing fullerene graphs from their eigenvalues and angles, Linear Algebra Appl. 356 (2002) 37–56.
[6] E. Estrad, Characterization of 3D molecular structure, Chem. Phys. Lett. 319 (2000) 713–718.
[7] G. H. Fath-Tabar, A. R. Ashrafi and D. Stevanovi´ c, Spectral properties of fullerenes, J. Comput. Theor. Nanosci. 9 (1) (2012) 327–329 .
[8] P. W. Fowler and D. E. Manolopoulos, An Atlas of Fullerenes, Clarendon Press, Oxford, 1995.
[9] M. Ghorbani and A. R. Ashrafi, Counting the Number of Hetero Fullerenes, J. Comput. Theor.Nanosci. 3 (2006) 803–810.

[10] M. Ghorbani, A. R. Ashrafi and M. Hemmasi, Eccentric Connectivity Polynomial of C18n+10 Fullerenes, Bulg. Chem. Commun. 45 (2013) 5–8.

[11] M. Ghorbani, M. Faghani, A. R. Ashrafi, S. Heidari-Rad and A. Graova´ c, An upper bound for energy of matrices associated to an infinite class of fullerenes, MATCH Commun. Math. Comput. Chem. 71 (2014) 341–354.
[12] M. Ghorbani and S. Heidari-Rad, Study of fullerenes by their Algebraic Properties, Iranian J. Math. Chem. 3 (2012) 9–24.
[13] M. Ghorbani and E. Naserpour, Study of some nanostructures by using their Kekul´ e structures, J. Comput. Theor. Nanosci. 10 (2013) 2260–2263.
[14] M. Ghorbani and M. Songhori, The enumeration of Hetero-fullerenes by Polya’s theorem, Fullerenes, Nanotubes and Carbon Nanostructures. J. Comput. Theor. Nanosci. 21 (2013) 460–471.
[15] M. Ghorbani and E. Bani-Asadi, Remarks on characteristic coefficients of fullerene graphs, Appl. Math. Comput. 230 (2014) 428–435.
[16] M. Ghorbani, Remarks on markaracter table of fullerene graphs. J. Comput. Theor. Nanosci. 11 (2014) 363–379.
[17] C. Godsil and G. Royle, Algebraic Graph Theory, Springer-Verlag, New York, 2001.
[18] A. Graova´ c, O. Ori, M. Faghani and A. R. Ashrafi, Distance property of fullerenes, Iranian J. Math. Chem. 2 (2011) 99–107.
[19] I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, 1986.
[20] I. Gutman, The energy of a graph, Ber. Math.-Statist. Sekt. Forsch. Graz 103 (1978) 1–22.
[21] F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
[22] H. W. Kroto, J. R. Heath, S. C. OBrien, R. F. Curl and R. E. Smalley, buckminster fullerene. Nature. 318 (1985) 162–163.
[23] H. W. Kroto, J. E. Fichier and D. E. Cox, The Fullerene, Pergamon Press, New York 1993.
[24] S. L. Lee, Y. L. Luo, B. E. Sagan and Y. -N. Yeh, Eigenvectors and eigenvalues of some special graphs, IV multilevel circulants. Int. J. Quant. Chem. 41 (1992) 105–116.
[25] W. C. Shiu, On the spectra of the fullerenes that contain a nontrivial cyclic-5-cutset, Australian J. Combin. 47 (2010) 41–51.