Local Distance Antimagic Labeling of Generalized Mycielskian Graphs
Why this work is in the frame
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Bibliographic record
Abstract
Let \(G=(V,E)\) be a graph of order \(n\) without isolated vertices. A bijection \(f\colon V\rightarrow \{1,2,\dots,n\}\) is called a local distance antimagic labeling, if \(w(u)\not=w(v)\) for every edge \(uv\) of \(G\), where \(w(u)=\sum_{x\in N(u)}f(x)\). The local distance antimagic chromatic number \(\chi_{ld}(G)\) is defined to be the minimum number of colors taken over all colorings of \(G\) induced by local distance antimagic labelings of \(G\). The concept of Generalized Mycielskian graphs was introduced by Stiebitz [20]. In this paper, we study the local distance antimagic labeling of the Generalized Mycielskian graphs.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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