Structural Exploration and Expected values of Topological Indices of Square-Hexagonal <i>T</i> <sub>2,3</sub> Kink Chains for Advanced Engineering Applications
Bibliographic record
Abstract
High Resolution Image Download MS PowerPoint Slide Square-hexagonal kink chains offer a compelling balance between geometric regularity and topological complexity, making them valuable models for studying molecular diversity in chemical graph theory. These structures, composed of alternating square and hexagonal polygons, introduce angular distortions and connectivity variations that significantly influence properties such as electronic behavior, entropy, and mechanical stability, characteristics relevant to graphene derivatives and polycyclic hydrocarbons. This work focuses on kink chains of type T 2,3, for which we construct four structural configurations by systematic polygonal attachments. For each configuration, we derive exact expressions for several topological indices, including geometric-arithmetic, Zagreb (first and second), Forgotten, sum-connectivity, product-connectivity, and atom bond-connectivity indices. In addition to deterministic values, we calculate exact expressions of expected values using a probabilistic vertex-weighting approach for these indices, thereby offering a statistical dimension to the structural analysis. Numerical evaluation, graphical visualization, and analytical comparison reveal trends and extremal indices across configurations. These findings deepen our understanding of how kink topology influences both exact and expected topological descriptors, supporting future applications in nanomaterial design and theoretical modeling.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".