Entire Neighborhood Topological Indices: Theory and Applications in Predicting Physico-Chemical Properties
Bibliographic record
Abstract
Topological indices are numerical descriptors that describe the chemical structures of chemical compounds using their molecular graphs. Recent advancements in topological indices have seen the emergence of neighborhood indices and entire topological indices, offering distinct perspectives on molecular structure. Neighborhood indices emphasize local atomic environments, while entire indices provide a comprehensive view by considering interactions between atoms, bonds, and their combinations. To achieve a more balanced and informative representation, we introduce 'entire neighborhood indices'. By integrating the localized focus of neighborhood indices within the framework of entire indices, these new descriptors offer a more complete picture of molecular structure and are expected to significantly enhance the accuracy of predictions for various molecular properties. In this paper, we introduce a new version of Zagreb topological indices named first, second, and modified entire neighborhood topological indices; denoted by \(NM_{1}^{\varepsilon}\), \(NM_{2}^{\varepsilon}\), and \(MNM_{1}^{\varepsilon}\), respectively. The structure-property regression analysis is used to investigate and compute the chemical significant of these newly introduced indices for the prediction of the physico-chemical properties of octane isomers and benzenoid hydrocarbons benchmark datasets. We analays and calculate the specific formulae of the entire neighborhood indices for several important graph families such as path, regular, cycle, complete, bipartite, book, gear and helm graph. Furthermore, we determine the exact value of these new indices for some types of bridge graphs and Sierpinski graphs.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".