STAR SUPER EDGE MAGIC DEFICIENCY OF GRAPHS
Why this work is in the frame
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Bibliographic record
Abstract
A graph G is called edge - magic if there is a bijec-tive function f : V (G)∪E(G) → {1, 2, . . . , |V (G)|+|E(G)|} such that for every edge xy ∈ E(G), f(x) + f(xy) + f(y) = c is a con-stant, called the valence of f. A graph G is said to be super edge - magic if f(V (G)) = {1, 2, . . . , |V (G)|}. Let G be a graph with p vertices with V (G) = {v1, v2, . . . , vp}. In G, every vertex vi is identified to the center vertex of Smi , for some mi ≥ 0, 1 ≤ i ≤ n, where S0 = K1 and the graph is denoted by G(m1,m2,...,mp). Let M(G) = {(m1,m2, . . . ,mp)|G(m1,m2,...,mp) is a super edge magic graph }. The star super edge magic deficiency Sμ∗(G) is defined as Sμ∗(G) = min(m1,,m2,...,mp)(m1 + m2 + · · · + mp) if M(G) 6= ∅; +∞ if M(G) = ∅. In this paper we determine the star super edge magic deficiency of certain classes of 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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| 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