Abstract
A (k,6)-fullerene graph is a planar 3-regular graph with k-polygon faces. In this chapter, we are going to obtain spectral moments of (k,6)-fullerene graph for kâ=â3,4,5 and use them for calculating the Estrada index of these graphs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
AleksiÄ T, Gutman I, PetroviÄ M (2007) Estrada index of iterated line graphs. Bull Academie Serbe des Sci et des Arts (Cl Math Natur) 134:33â41
Ashrafi AR, FathâTabar GH (2011) Bounds on the Estrada index of ISR (4,6)âââfullerenes. Appl Math Lett 24:337â339
Balasubramanian K (1994) Laplacian polynomials of fullerenes (C20âââC40). Chem Phys Lett 224:325â332
Behmaram A (2013) Matching in fullerene and molecular graphs. Ph.D. thesis, University of Tehran
CvetkoviÄ D, StevankoviÄ D (2004) Spectral moments of fullerene graphs. MATCH Commun Math Comput Chem 50:62â72
CvetkoviÄ D, Doob M, Sachs H (1995) Spectra of graphsâââtheory and application, 3rd edn. Johann Ambrosius Barth Verlag, Heidelberg/Leipzig
De La Pena JA, Gutman I, Rada J (2007) Estimating the Estrada index. Linear Algebra Appl 427:70â76
Estrada E (2000) Characterization of 3D molecular structure. Chem Phys Lett 319:713â718
Estrada E (2002) Characterization of the folding degree of proteins. Bioinformatics 18:697â704
Estrada E (2004) Characterization of the amino acid contribution to the folding degree of proteins. Proteins 54:727â737
Estrada E (2007) Topological structural classes of complex networks. Phys Rev 75:016103
Estrada E, RodriguezâââValazquez JA, RandiÄ M (2006) Atomic branching in molecules. Int J Quantum Chem 106:823â832
FathâTabar GH, Ashrafi AR (2010) Some remarks on Laplacian eigenvalues and Laplacian energy of graphs. Math Commun 15:443â451
FathâTabar GH, Ashrafi AR (2011) New upper bounds for Estrada index of bipartite graphs. Linear Algebra Appl 435:2607â2611
FathâTabar GH, Ashrafi AR, Gutman I (2008) Note on Laplacian energy of graphs. Bulletin de lâAcademie Serbe des Sciences et des Arts 137:1â10
FathâTabar GH, Ashrafi AR, Gutman I (2009) Note on Estrada and LâââEstrada indices of graphs. Bulletin del Academie Serbe des Sciences et des Arts 139:1â16
Fath-Tabar GH, Ashrafi AR, Stevanovic D (2012) Spectral properties of fullerenes. J Comput Theor Nanosci 9:1â3
Fowler PW, Manolopoulos DE (1995) An atlas of fullerenes. Oxford University Press, New York
Gutman I, RadenkoviÄ S (2007a) A lower bound for the Estrada index of bipartite molecular graphs. Kragujevac J Sci 29:67â72
Gutman I, RadenkoviÄ S (2007b) Estrada index of benzenoid hydrocarbons. Z Naturforschung 62a:254â258
Gutman I, Furtula B, MarkoviÄ V, GliĊĦiÄ B (2007a) Alkanes with greatest Estrada index. ZNaturforsch 62a:495â498
Gutman I, RadenkoviÄ S, Furtula B, Mansour T, Schork M (2007b) Relating Estrada index with spectral radius. J Serb Chem Soc 72:1321â1327
Gutman I, Furtula B, GliĊĦic B, MarkoviÄ V, Vesel A (2007c) Estrada index of acyclic molecules. Indian J Chem 46a:723â728
Kroto HW, Heath JR, OâBrien SC, Curl RF, Smalley RE (1985) C60 Buckminster fullerene. Nature 318:162â163
Kroto HW, Fichier JE, Cox DE (1993) The fullerene. Pergamon Press, New York
Mehranian Z, Gholami A, Ashrafi AR (2014) Experimental results on the symmetry and topology of 3â and 4âââgeneralized fullerenes. J Comput Theor Nanosci 11:2283â2288
Myrvold W, Bultena B, Daugherty S, Debroni B, Girn S, Minchenko M, Woodcock J, Fowler PW (2007) A graphical user interface for investigating conjectures about fullerenes. MATCH Commun Math Comput Chem 58:403â422
Taghvaee F, Ashrafi AR (2016) Comparing fullerenes by spectral moments. J Nanosci Nanotechnol 16:3132â3135
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Âİ 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Fath-Tabar, G.H., Taghvaee, F., Javarsineh, M., Graovac, A. (2016). The Spectral Moments of a Fullerene Graph and Their Applications. In: Ashrafi, A., Diudea, M. (eds) Distance, Symmetry, and Topology in Carbon Nanomaterials. Carbon Materials: Chemistry and Physics, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-31584-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-31584-3_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-31582-9
Online ISBN: 978-3-319-31584-3
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)