Laplacian and signless-laplacian energies of closed shadow graphs
In 2005, I. Gutman and B. Zhou introduced the notion of Laplacian energy, which is defined as the sum of the differences between the Laplacian eigenvalues of the graph and the average degree of vertices in the graph. In this study, we determine the Laplacian eigenvalues of the closed shadow graphs o...
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| Format: | text |
| Language: | English |
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Animo Repository
2022
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| Online Access: | https://animorepository.dlsu.edu.ph/etdb_math/17 https://animorepository.dlsu.edu.ph/cgi/viewcontent.cgi?article=1011&context=etdb_math |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | In 2005, I. Gutman and B. Zhou introduced the notion of Laplacian energy, which is defined as the sum of the differences between the Laplacian eigenvalues of the graph and the average degree of vertices in the graph. In this study, we determine the Laplacian eigenvalues of the closed shadow graphs of different families of graphs. Thus, also determining the Laplacian energy of the closed shadow graphs of different families of graphs. In addition, we find the relationship between the Laplacian energy of any graph and the Laplacian energy of its closed shadow graph. |
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