On the energy of closed shadow graphs
The energy and d-energy of a graph is the sum of the absolute value of eigenvalues of the graph’s adjacency matrix and distance matrix respectively. In 2017, S. Vaidya and K. Popat determined the energy of a shadow graph of a connected graph. In this study, we determine the eigenvalues and d-eigenva...
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oai:animorepository.dlsu.edu.ph:etdm_math-10102024-04-25T02:46:48Z On the energy of closed shadow graphs Morisca, Melody Mae L. The energy and d-energy of a graph is the sum of the absolute value of eigenvalues of the graph’s adjacency matrix and distance matrix respectively. In 2017, S. Vaidya and K. Popat determined the energy of a shadow graph of a connected graph. In this study, we determine the eigenvalues and d-eigenvalues of a closed shadow graph and closed m-shadow graph. Using those spectrum and distance spectrum that we obtained, we computed the energy and distance energy of closed shadow graph and closed m-shadow graph. We also introduce a new graph operation called anti-shadow of a graph and determine the spectrum of the graph obtained from the graph operator. 2024-01-01T08:00:00Z text application/pdf https://animorepository.dlsu.edu.ph/etdm_math/11 https://animorepository.dlsu.edu.ph/context/etdm_math/article/1010/viewcontent/2024_Morisca_On_the_energy_of_closed_shadow_graphs_Full_text.pdf Mathematics and Statistics Master's Theses English Animo Repository Force and energy Graph theory Mathematical analysis Mathematics |
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Force and energy Graph theory Mathematical analysis Mathematics |
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Force and energy Graph theory Mathematical analysis Mathematics Morisca, Melody Mae L. On the energy of closed shadow graphs |
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The energy and d-energy of a graph is the sum of the absolute value of eigenvalues of the graph’s adjacency matrix and distance matrix respectively. In 2017, S. Vaidya and K. Popat determined the energy of a shadow graph of a connected graph. In this study, we determine the eigenvalues and d-eigenvalues of a closed shadow graph and closed m-shadow graph. Using those spectrum and distance spectrum that we obtained, we computed the energy and distance energy of closed shadow graph and closed m-shadow graph. We also introduce a new graph operation called anti-shadow of a graph and determine the spectrum of the graph obtained from the graph operator. |
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text |
| author |
Morisca, Melody Mae L. |
| author_facet |
Morisca, Melody Mae L. |
| author_sort |
Morisca, Melody Mae L. |
| title |
On the energy of closed shadow graphs |
| title_short |
On the energy of closed shadow graphs |
| title_full |
On the energy of closed shadow graphs |
| title_fullStr |
On the energy of closed shadow graphs |
| title_full_unstemmed |
On the energy of closed shadow graphs |
| title_sort |
on the energy of closed shadow graphs |
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Animo Repository |
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2024 |
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https://animorepository.dlsu.edu.ph/etdm_math/11 https://animorepository.dlsu.edu.ph/context/etdm_math/article/1010/viewcontent/2024_Morisca_On_the_energy_of_closed_shadow_graphs_Full_text.pdf |
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