Computing graph energy: An alternative approach
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Kragujevac, Faculty of Science
2014-01-01
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| Series: | Kragujevac Journal of Science |
| Online Access: | http://scindeks-clanci.ceon.rs/data/pdf/1450-9636/2014/1450-96361436069F.pdf |
| Summary: | 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. |
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| ISSN: | 1450-9636 2466-5509 |