Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes

Open access


The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.

[1] A. Cantoni and P. Buter, Eigenvalues and eigenvectors of symmetric centrosymmet- ric matrices, Linear Algebra Appl. 13 (1976) 275-288. doi:10.1016/0024-3795(76)90101-4

[2] D. Cvetković, M. Doob, I. Gutman and A. Torgašev, Recent Results in the Theory of Graph Spectra (North-Holland Publishing Co., Amsterdam, 1988).

[3] D. Cvetković, P. Rowlinson and S. Simić, An Introduction to the Theory of Graph Spectra (Cambridge University Press, Cambridge, 2010).

[4] P.W. Fowler and D.E. Manolopoulos, An Atlas of Fullerenes (Clarendom Press, Oxford, 1995).

[5] P.W. Fowler and W. Myrvold, Most fullerenes have no centrosymmetric labelling, MATCH Commun. Math. Comput. Chem. 71 (2014) 93-97.

[6] A. Graovac, O. Ori, M. Faghani and A.R. Ashrafi, Distance property of fullerenes, Iranian J. Math. Chem. 2 (2011) 99-107.

[7] I. Gutman, The energy of a graph, Ber. Math.-Statist. Sekt. Forsch. Graz 103 (1978) 1-22.

[8] I. Gutman, Bounds for all graph energies, Chem. Phys. Lett. 528 (2012) 72-74.

[9] I. Gutman and B. Zhou, Laplacian energy of a graph, Linear Algebra Appl. 414 (2006) 29-37. doi:10.1016/j.laa.2005.09.008

[10] I. Gutman, S. Zare Firoozabadi, J.A. de la Peña and J. Rada, On the energy of regular graphs, MATCH Commun. Math. Comput. Chem. 57 (2007) 435-442.

[11] H. Hua, M. Faghani and 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.

[12] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl and R.E. Smalley, C60 : buckmin- sterfullerene, Nature 318 (1985) 162-163. doi:10.1038/318162a0

[13] Z. Liu and H. Faßbender, Some properties of generalized K-centrosymmetric H- matrices, J. Comput. Appl. Math. 215 (2008) 38-48. doi:10.1016/j.cam.2007.03.026

[14] Z.-Y. Liu, Some properties of centrosymmetric matrices, Appl. Math. Comput. 141 (2003) 297-306. doi:10.1016/S0096-3003(02)00254-0

[15] V. Nikiforov, The energy of graphs and matrices, J. Math. Anal. Appl. 326 (2007) 1472-1475. doi:10.1016/j.jmaa.2006.03.072

[16] O. Rojo and H. Rojo, Some results on symmetric circulant matrices and on sym- metric centrosymmetric matrices, Linear Algebra Appl. 392 (2004) 211-233. doi:10.1016/j.laa.2004.06.013

Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

Journal Information

IMPACT FACTOR 2017: 0.601
5-year IMPACT FACTOR: 0.535

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.763
Source Normalized Impact per Paper (SNIP) 2018: 0.934

Mathematical Citation Quotient (MCQ) 2017: 0.36

Target Group

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 136 116 8
PDF Downloads 44 38 4