Analytical Expressions and Structural Characterization of Some Molecular Models Through Degree Based Topological Indices
Bibliographic record
Abstract
This article explores a practical applications of chemical graph theory in the field of physical chemistry.Chemical graph theory is a branch of mathematics that uses mathematical techniques to correlate the structural characteristics of molecules.By applying these methods, scientists can better understand how different molecules behave and interact in the world of chemistry.Topological indices, which are two/threedimensional descriptors of the internal atomic organization of compounds, provide valuable information about the size, shape, branching, presence of heteroatoms, and number of bonds in a given molecular structure.This article highlights the importance of topological indices in understanding the physical properties and behavior of molecules, and how they can be used in various applications such as drug design, material science, and catalysis.In this article, we computed irregularity topological indices for the Oxide network (𝑂𝑋 𝑛 ), Silicate network (𝑆𝐿 𝑛 ), Chain silicate (𝐶𝑆 𝑛 ), and honeycomb network (𝐻𝐶 𝑛 ).The 3D comparison graphs are also investigated.The article concludes with a discussion of the challenges and future directions in the field of chemical graph theory.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".