ON SUPER (a, 2)-EDGE-ANTIMAGIC TOTAL LABELING OF DISCONNECTED GRAPHS
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
A labeling of a graph is a mapping that carries some set of graph elements into numbers (usually the positive integers). An (a, d)-edge-antimagic total labeling of a graph with p vertices and q edges is a one-to-one mapping that takes the vertices and edges onto the integers 1, 2, ... ,p + q, such that the sums of the label on the edges and the labels of their end points form an arithmetic sequence starting from a and having a common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper we study the super (a, 2)-edge-antimagic total labelings of disconnected graphs. We also present some necessary conditions for the existence of (a, d)-edge-antimagic total labelings for d even.
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.
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