Diminished Sombor index and its relationship with topological indices
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909730515976192 |
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| author | Movahedi, F. |
| author_facet | Movahedi, F. |
| contents | In this paper, we investigate the Diminished Sombor index (DSO), a recently introduced degree-based topological index for a simple graph $G$, defined as \[ DSO(G) = \sum_{uv \in E} \frac{\sqrt{d_u^2+d_v^2}}{d_u+d_v}, \] where $d_u$ denotes the degree of a vertex $u \in V$. We establish several sharp bounds for this index in terms of classical topological indices such as the Zagreb, Albertson, Harmonic, Randić, and geometric-arithmetic indices. The relationships and inequalities between DSO and these indices are analyzed thoroughly, with characterizations of extremal graphs achieving equality conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_06532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diminished Sombor index and its relationship with topological indices Movahedi, F. Combinatorics topological index, Diminished Sombor index, degree-based index, Chemical graph theory In this paper, we investigate the Diminished Sombor index (DSO), a recently introduced degree-based topological index for a simple graph $G$, defined as \[ DSO(G) = \sum_{uv \in E} \frac{\sqrt{d_u^2+d_v^2}}{d_u+d_v}, \] where $d_u$ denotes the degree of a vertex $u \in V$. We establish several sharp bounds for this index in terms of classical topological indices such as the Zagreb, Albertson, Harmonic, Randić, and geometric-arithmetic indices. The relationships and inequalities between DSO and these indices are analyzed thoroughly, with characterizations of extremal graphs achieving equality conditions. |
| title | Diminished Sombor index and its relationship with topological indices |
| topic | Combinatorics topological index, Diminished Sombor index, degree-based index, Chemical graph theory |
| url | https://arxiv.org/abs/2508.06532 |