Vertex energies of splitting and shadow graphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908902211190784 |
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| author | A, Harshitha K V, Madhumitha D'Souza, Sabitha |
| author_facet | A, Harshitha K V, Madhumitha D'Souza, Sabitha |
| contents | Graph energy has been widely investigated in spectral graph theory. However, the manner in which this energy is distributed among individual vertices has received attention only more recently, following the introduction of energy of a vertex by O. Arizmendi et al. in 2018. Since then, several studies have explored this concept. In the present work, we focus on splitting graphs and shadow graphs and study how the total energy of a graph is distributed among its vertices. We further establish explicit expressions for vertex energies in these derived structures and analyze their behavior in comparison with the underlying graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19590 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vertex energies of splitting and shadow graphs A, Harshitha K V, Madhumitha D'Souza, Sabitha Combinatorics 05C50 Graph energy has been widely investigated in spectral graph theory. However, the manner in which this energy is distributed among individual vertices has received attention only more recently, following the introduction of energy of a vertex by O. Arizmendi et al. in 2018. Since then, several studies have explored this concept. In the present work, we focus on splitting graphs and shadow graphs and study how the total energy of a graph is distributed among its vertices. We further establish explicit expressions for vertex energies in these derived structures and analyze their behavior in comparison with the underlying graph. |
| title | Vertex energies of splitting and shadow graphs |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2603.19590 |