Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes

Gyula Y. Katona; Morteza Faghani; Ali Reza Ashrafi

Discussiones Mathematicae Graph Theory (2014)

  • Volume: 34, Issue: 4, page 751-768
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Gyula Y. Katona, Morteza Faghani, and Ali Reza Ashrafi. "Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes." Discussiones Mathematicae Graph Theory 34.4 (2014): 751-768. <http://eudml.org/doc/269815>.

@article{GyulaY2014,
abstract = {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.},
author = {Gyula Y. Katona, Morteza Faghani, Ali Reza Ashrafi},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {centrosymmetric matrix; fullerene graph; energy.; energy},
language = {eng},
number = {4},
pages = {751-768},
title = {Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes},
url = {http://eudml.org/doc/269815},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Gyula Y. Katona
AU - Morteza Faghani
AU - Ali Reza Ashrafi
TI - Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 4
SP - 751
EP - 768
AB - 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.
LA - eng
KW - centrosymmetric matrix; fullerene graph; energy.; energy
UR - http://eudml.org/doc/269815
ER -

References

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  1. [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. [2] D. Cvetković, M. Doob, I. Gutman and A. Torgašev, Recent Results in the Theory of Graph Spectra (North-Holland Publishing Co., Amsterdam, 1988). Zbl0634.05054
  3. [3] D. Cvetković, P. Rowlinson and S. Simić, An Introduction to the Theory of Graph Spectra (Cambridge University Press, Cambridge, 2010). Zbl1211.05002
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  5. [5] P.W. Fowler and W. Myrvold, Most fullerenes have no centrosymmetric labelling, MATCH Commun. Math. Comput. Chem. 71 (2014) 93-97. 
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  10. [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. Zbl1150.05024
  11. [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. [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. [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 Zbl1142.65033
  14. [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. [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 Zbl1113.15016
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