On Randić energy of a vertex
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908561623220224 |
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| author | Gogoi, Idweep J. Buragohain, J. Bharali, A. Devi, E. |
| author_facet | Gogoi, Idweep J. Buragohain, J. Bharali, A. Devi, E. |
| contents | In 2018, Arizmendi and Juarez introduced the concept of energy of a vertex, a novel approach allowing the total energy of a graph to be expressed as the sum of the energies of its individual vertices. In this article, we extend the notion of energy of a vertex to the context of the Randić matrix. We define the Randić energy of a vertex and explore its mathematical properties through various combinatorial techniques. We derive several upper and lower bounds for the Randić energy of a vertex. Furthermore, we establish that among the connected graphs, the central vertex of a star attains the maximum Randić energy, whereas pendent vertices attain the minimum. Also, we report the Coulson-type integral formula for the Randić energy of a vertex and its applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Randić energy of a vertex Gogoi, Idweep J. Buragohain, J. Bharali, A. Devi, E. Spectral Theory 5C50, 05C07, 15A18 In 2018, Arizmendi and Juarez introduced the concept of energy of a vertex, a novel approach allowing the total energy of a graph to be expressed as the sum of the energies of its individual vertices. In this article, we extend the notion of energy of a vertex to the context of the Randić matrix. We define the Randić energy of a vertex and explore its mathematical properties through various combinatorial techniques. We derive several upper and lower bounds for the Randić energy of a vertex. Furthermore, we establish that among the connected graphs, the central vertex of a star attains the maximum Randić energy, whereas pendent vertices attain the minimum. Also, we report the Coulson-type integral formula for the Randić energy of a vertex and its applications. |
| title | On Randić energy of a vertex |
| topic | Spectral Theory 5C50, 05C07, 15A18 |
| url | https://arxiv.org/abs/2509.22539 |