Abstract
Estrada Index, EE(G), defined as the sum of exponentials of the eigenvalues of the adjacency matrix of graph G, is calculated for sets of general cubic polyhedra, and for general and isolated-pentagon fullerenes. Amongst small cubic polyhedra, the “near-fullerenes” and fullerenes minimise EE. Amongst fullerenes, the isolated-pentagon fullerenes minimise EE. The preference for fullerenes over non-fullerenes is significant, but the relative variation of EE with fullerene isomer is tiny (parts per million for general fullerenes, parts per billion for isolated-pentagon fullerenes) and is essentially tracking the number of pentagon adjacencies (and hence overall stability).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brinkmann G, Dress AWM (1997) J Algorithms 23:345–358 A constructive enumeration of fullerenes
Brinkmann G, Dress AWM (1998) Adv App Math 21:473–480 PentHex Puzzles: A Reliable and Efficient Top-Down Approach to Fullerene-Structure Enumeration
de la Peña JA,. Gutman I, Rada J (2007) Linear Alg Appl 427:70–76 Estimating the Estrada Index
Domene MC, Fowler PW, Mitchell D, Seifert G, Zerbetto F (1997) J Phys Chem A 101:8339–8344 Energetics of C20 and C22 fullerene and near-fullerene carbon cages
Došlić T (2005) Chem Phys Lett 412:336–340 Bipartivity of fullerene graphs and fullerene stability
Estrada E (2000) Chem Phys Lett 319:713–718 Characterization of 3D molecular structure
Estrada E (2002) Bioinformatics 18:697–704 Characterization of the folding degree of proteins
Estrada E (2004) Proteins 54:727–737 Characterization of the amino acid contribution to the folding degree of proteins
Estrada E, Hatano N (2007) Chem Phys Lett 439:247–251 Statistical-mechanical approach to subgraph centrality in complex networks
Estrada E, Rodríguez-Velázquez JA (2005a) Phys Rev E 71:056103 (1–9) Subgraph centrality in complex networks
Estrada E, Rodríguez-Velázquez JA (2005b) Phys Rev E 72:046105 (1–6) Spectral measures of bipartivity in complex networks
Estrada E, Rodríguez-Velázquez JA, Randić M (2006) Int J Quantum Chem 106:823–832 Atomic branching in molecules
Fowler PW (2002) Croat Chem Acta 75:401–408 Resistance distances in fullerene graphs
Fowler PW (2003) MATCH Commun Math Comput Chem 48:87–96 Complexity, Spanning Trees and Relative Energies in Fullerene Isomers
Fowler PW, Manolopoulos DE (1995) An atlas of fullerenes. Clarendon Press, Oxford. Reprinted: Dover, New York, NY (2006)
Ginosar YI, Gutman IT, Mansour TM, Schork M (2008) Chem Phys Lett 454:145–147 Estrada Index and Chebyshev polynomials
Grünbaum B, Motzkin TS (1963) Can J Math 15:744–751 The number of hexagons and the simplicity of geodesics on certain polyhedra
Gutman I, Estrada E, Rodríguez-Velázquez JA (2007a) Croat Chem Acta 80:151–154 On a graph-spectrum-based structure descriptor
Gutman I, Furtula B, Glisić B, Marković V, Vesel A (2007b) Indian J Chem A 46:723–728 Estrada Index of acyclic molecules
Gutman I, Graovac A (2007c) Chem Phys Lett 436:294–296 Estrada Index of cycles and paths
Gutman I, Radenković S (2007d) Z f Naturforsch A 62:254–258 Estrada Index of benzenoid hydrocarbons
Gutman I, Radenković S, Furtula B, Mansour T, Schork M (2007e) J Serbian Chem Soc 72:1321–1327 Relating Estrada Index with spectral radius
Gutman I, Radenković S, Graovac A, Plavšić D (2007f) Chem Phys Lett 446:233–236 Monte Carlo approach to Estrada Index
Manolopoulos DE, May JC, Down SE (1991) Chem Phys Lett 181:105–111. Theoretical studies of the fullerenes:C34–C70
Schwenk AJ (1979) Ann NY Acad Sci 328:183–189 Spectral reconstruction problems
Zhang H, Balasubramanian K (1993) J Phys Chem 97:1034110345 Analytical expressions for the moments and characteristic polynomials of fullerenes containing isolated pentagons
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Netherlands
About this chapter
Cite this chapter
Fowler, P.W., Graovac, A. (2011). The Estrada Index and Fullerene Isomerism. In: Cataldo, F., Graovac, A., Ori, O. (eds) The Mathematics and Topology of Fullerenes. Carbon Materials: Chemistry and Physics, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0221-9_14
Download citation
DOI: https://doi.org/10.1007/978-94-007-0221-9_14
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0220-2
Online ISBN: 978-94-007-0221-9
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)