Metrika članka

  • citati u SCindeksu: 0
  • citati u CrossRef-u:[1]
  • citati u Google Scholaru:[=>]
  • posete u poslednjih 30 dana:5
  • preuzimanja u poslednjih 30 dana:5
članak: 1 od 1  
Kragujevac Journal of Science
2014, br. 36, str. 69-78
jezik rada: engleski
vrsta rada: neklasifikovan

Computing graph energy: An alternative approach
(naslov ne postoji na srpskom)
aCenter for Separation Processes Modeling and Nano-Computations, School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, Iran
bUniverzitet u Kragujevcu, Prirodno-matematički fakultet
cCenter for Separation Processes Modeling and Nano-Computations, School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, Iran + Oil and Gas Center of Excellence, University of Tehran, Tehran, Iran



(ne postoji na srpskom)
The characteristic polynomial corresponding to the adjacency matrix of a graph is obtained by the Faddeev-Leverrier algorithm. Subsequently, an improved numerical scheme, based on the Newton-Raphson algorithm and the Adomian decomposition method, is applied to calculate the energy of the graph (the HMO total π-electron energy of a conjugated molecule). In addition, a nonlinear convergence accelerator, known as the Shanks transform, is employed to speed-up the calculation process. The proposed scheme is conceptually easy, straightforward, and shown to be superior to the classic Newton-Raphson algorithm in terms of computational volume.


Abbaoui, K., Cherruault, Y. (1994) Convergence of Adomian's method applied to nonlinear equations. Math. Comput. Model, 9, 69-73
Abbasbandy, S. (2003) Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method. Applied Mathematics and Computation, 145(2-3): 887-893
Adomian, G. (1994) Solving frontier problems of physics: The decomposition method. Dordrecht, itd: Kluwer Academic Press
Adomian, G. (1990) A review of the decomposition method and some recent results for nonlinear equations. Math. Comput. Model, 13, 17-43
Babolian, E., Biazar, J. (2002) On the order of convergence of Adomian method. Applied Mathematics and Computation, 130(2-3): 383-387
Balasubramanian, K. (1984) The use of Frame's method for the characteristic polynomials of chemical graphs. Theor. Chim. Acta, 65, 49-58
Balasubramanian, K. (1984) The use of Frame's method for characteristic polynomial of chemical graphs. J. Comput. Chem, 5, 387-394
Balasubramanian, K. (1988) Computer generation of characteristic polynomials of edge-weighted graphs, heterographs, and directed graphs. Journal of Computational Chemistry, 9(3): 204-211
Dias, J.R. (1993) Molecular Orbital Calculations Using Chemical Graph Theory. Berlin, Heidelberg: Springer Nature America, Inc
Fatoorehchi, H., Abolghasemi, H. (2011) On calculation of Adomian polynomials by MATLAB. J. Appl. Comput Sci. Math., 5, 85-88
Fatoorehchi, H., Abolghsemi, H. (2011) Adomian decomposition method to study mass transfer from a horizontal flat plate subject to laminar fluid flow. Adv. Nat. Appl. Sci, 5, 26-33
Fatoorehchi, H., Abolghasemi, H. (2013) A more realistic approach toward the differential equation governing the glass transition phenomenon. Intermetallics, 32: 35-38
Fatoorehchi, H., Abolghasemi, H. (2013) Improving the differential transform method: A novel technique to obtain the differential transforms of nonlinearities by the Adomian polynomials. Applied Mathematical Modelling, 37(8): 6008-6017
Fatoorehchi, H., Abolghasemi, H., Rach, R. (2014) An accurate explicit form of the Hankinson-Thomas-Phillips correlation for prediction of the natural gas compressibility factor. Journal of Petroleum Science and Engineering, 117: 46-53
Graovac, A., Gutman, I., Trinajstić, N. (1977) Topological Approach to the Chemistry of Conjugated Molecules. Berlin, Heidelberg: Springer Nature America, Inc
Gutman, I. (1978) The energy of a graph. Ber. Math. Statist. Sekt. Forschungsz, Graz, 103, 1-22
Gutman, I. (2003) Impact of the Sachs theorem on theoretical chemistry. Communications in Mathematical and in Computer Chemistry / MATCH, br. 48, str. 17-34
Gutman, I. (2005) Topology and stability of conjugated hydrocarbons: The dependence of total π-electron energy on molecular topology. Journal of the Serbian Chemical Society, vol. 70, br. 3, str. 441-456
Helmberg, G., Wagner, P., Veltkamp, G. (1993) On Faddeev-Leverrier's method for the computation of the characteristic polynomial of a matrix and of eigenvectors. Linear Algebra and its Applications, 185: 219-233
Householder, A.S. (1964) The theory of matrices in numerical analysis. New York: Blaisdell
Krivka, P., Jeričević, Ž., Trinajstić, N. (1986) On the computation of characteristic polynomial of a chemical graph. Int. J. Quantum Chem. Quantum Chem. Symp., 19, 129-147
Kundu, B., Wongwises, S. (2012) A decomposition analysis on convecting-radiating rectangular plate fins for variable thermal conductivity and heat transfer coefficient. Journal of the Franklin Institute, 349(3): 966-984
Li, X., Shi, Y., Gutman, I., Li, X., Shi, Y., Gutman, I. (2012) Introduction. u: Graph Energy, New York, NY: Springer Nature America, Inc, str. 1-9
Rach, R. (2012) A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011. Kybernetes, 41, 1087-1148
Randić, M. (1987) On the evaluation of the characteristic polynomial via symmetric function theory. J. Math. Chem, 1, 145-152
Shanks, D. (1955) Nonlinear transformation of divergent and slowly convergent sequences. J. Math. Phys. Sci, 34, 1-42
Trinajstić, N. (1977) Computing the characteristic polynomial of a conjugated system using the Sachs theorem. Croat. Chem. Acta, 49, 539-633
Vahidi, A.R., Jalalvand, B. (2012) Improving the accuracy of the Adomian decomposition method for solving nonlinear equations. Appl. Math. Sci, 6, 487-497