Maximum Diminished Sombor Index of Molecular Trees with a Perfect Matching
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915691437752320 |
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| author | Guo, Fei Wang, Fangxia |
| author_facet | Guo, Fei Wang, Fangxia |
| contents | The diminished Sombor index $(DSO)$ of a graph $G$, introduced by Rajathagiri, is defined as $$DSO(G)=\sum_{uv\in E}\frac{\sqrt{d_u^2+d_v^2}}{d_u+d_v},$$ where $d_u$ and $d_v$ are the degrees of vertices $u$ and $v$. A graph $G$ is a molecular graph if $d_G(u)\leq 4$ for all $u\in V(G)$. In this paper, we examine the chemical applicability of the $DSO$ index for predicting physicochemical properties of octane isomers. We also determine the maximum value of the diminished Sombor index among all molecular trees of order $n$ with perfect matching and characterize all the corresponding extremal trees. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_19710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum Diminished Sombor Index of Molecular Trees with a Perfect Matching Guo, Fei Wang, Fangxia Chemical Physics The diminished Sombor index $(DSO)$ of a graph $G$, introduced by Rajathagiri, is defined as $$DSO(G)=\sum_{uv\in E}\frac{\sqrt{d_u^2+d_v^2}}{d_u+d_v},$$ where $d_u$ and $d_v$ are the degrees of vertices $u$ and $v$. A graph $G$ is a molecular graph if $d_G(u)\leq 4$ for all $u\in V(G)$. In this paper, we examine the chemical applicability of the $DSO$ index for predicting physicochemical properties of octane isomers. We also determine the maximum value of the diminished Sombor index among all molecular trees of order $n$ with perfect matching and characterize all the corresponding extremal trees. |
| title | Maximum Diminished Sombor Index of Molecular Trees with a Perfect Matching |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2512.19710 |