Fuzzy Anti-Magic Labeling on Comb and Twing Graphs
Why this work is in the frame
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Bibliographic record
Abstract
Fuzzy labeling in graph theory is important because it enhances the modelling of uncertainties, gives relationships a granular representation, makes network models more robust, enables clustering and community detection, contributes to decisionmaking, enables machine learning and data mining, and has applications in different fields where complex structures need to be expressed with degrees of membership or uncertainty.In this paper, we proved that the twing and comb graphs admit fuzzy labeling by providing an algorithm.Also, we show that the twing and comb graphs reveal vertex and edge anti-magic labeling.Fuzzy end vertex, fuzzy bridge, degree, strong degree, and strong edge are mostly related to connectivity, so they may be applied to networking.Because of that, we have derived some properties related to the fuzzy end vertex, fuzzy bridge, degree, strong degree, and strong edge have been discussed.
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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 | 0.001 | 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 | 0.001 | 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 it