Odd harmonious labeling on squid graph and double squid graph
Why this work is in the frame
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Bibliographic record
Abstract
Abstract An injective function f from set of vertices in graph G to a set of {0,1,…,| E | − 1} is called an odd harmonious labeling if the function f induced the edge function f * from the set of edges of G to a set of odd positive integer number {1,3,5,…,2| E | − 1} with f *( xy ) = f ( x ) + f ( y ) for every edge xy in E. Graph that has an odd harmonious labeling is called odd harmonious graph. The squid graph T n,k is a graph which is obtained from a cycle C n and we add k pendant to one vertex of the cycle. It is known that C n is an odd harmonious graph if and only if n = 0 mod 4. However, by adding at least one pendant in the cycle graph, we can label the new graph odd harmoniously for all even number of vertices. In this paper, we showed that the graph T n,k and T 2 n,k are an odd harmonious graph, for n = 0 (mod 2), n ≥ 4 and k ≥ 1. The construction of the odd harmonious labeling of the graph T n,k and T 2 n,k are inspired by the odd harmonious labeling of C n for n = 0(mod 4).
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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 | 0.001 |
| 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