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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| Format: | text |
| Language: | English |
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Animo Repository
2024
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| Online Access: | 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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| Institution: | De La Salle University |
| Language: | English |
| Summary: | 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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