Article
| Title: | Structural properties and applications of the augmented Sombor index (English) |
| Author: | Xu, Chunlei |
| Author: | Das, Kinkar Chandra |
| Author: | Bera, Jayanta |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 3 |
| Year: | 2026 |
| Pages: | 1077-1110 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Topological indices are key quantitative descriptors in mathematical chemistry, unchanged under symmetry operations and retaining graph connectivity; they capture molecular structural features to provide insights into molecular stability and chemical properties, becoming indispensable in cheminformatics and theoretical chemistry. Among degree-based indices, the Sombor index is widely concerned for capturing structural information, and motivated by enhanced structural discrimination, the augmented Sombor index (ASO) is defined for a connected graph $\Omega $ with $|V(\Omega )|\geq 3$ as $$ {\rm ASO} (\Omega ) = \sum _{v_iv_j\in E(\Omega )} \sqrt {\frac {{d_i^2 + d_j^2}}{d_i + d_j - 2}}, $$ where $d_i$ and $d_j$ are the degrees of vertices $v_i$ and $v_j$, respectively. Within the scope of this study, we first establish several sharp bounds for the augmented Sombor index and characterize the extremal graphs attaining these bounds. In particular, we determine the minimum value of the ASO index for unicyclic graphs with a prescribed girth and characterize all graphs achieving this minimum. We also identify the second maximum ASO value among trees and characterize the corresponding extremal tree structures. Furthermore, the minimum and maximum values of the ASO index for bipartite graphs and chemical graphs are obtained, together with a complete characterization of the associated extremal graphs. In addition, we characterize the chemical trees that maximize the ASO index. The chemical applicability of the ASO index is investigated through quantitative structure-property relationship (QSPR) analysis, supported by a comparative assessment of several variants of the Sombor index. Finally, we present concluding remarks and outline potential directions for future research on the augmented Sombor index of graphs. (English) |
| Keyword: | augmented Sombor index |
| Keyword: | uncicyclic graph |
| Keyword: | tree |
| Keyword: | chemical graph |
| Keyword: | QSPR analysis |
| MSC: | 05C07 |
| MSC: | 05C09 |
| MSC: | 05C35 |
| DOI: | 10.21136/CMJ.2026.0111-26 |
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| Date available: | 2026-09-11T13:18:51Z |
| Last updated: | 2026-09-14 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153743 |
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