Integer Cordial Labelling on Graphs nF_(m_i ) (n-1) P_t With m_i Even or Odd
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Bibliographic record
Abstract
This paper discusses the integer cordial labeling on the graph nF_(m_i)(n-1)P_t when m_i is even or odd. The graph nF_m(n-1)P_t is obtained from n friendship graphs connected by n-1 paths P_t at vertices other than the central vertex of the graph for the i-th and i+1-th graphs where 1≤i≤n. Additionally, m_i denotes the number of copies of the cycle C_3 for each friendship graph. The main result is the integer cordial label for this graph. Furthermore, it was proved that nF_m(n-1)P_t when m_i even or odd is a graph with integer cordial labeling.
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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 | 0.005 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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