Irregularity Strength of Corona Product of a Graph with Star Graph
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Bibliographic record
Abstract
If positive weights are assigned to the edges of a graph $G$, then degree of a vertex is the sum of the weights of edges that are incident to the vertex. A graph with weighted edges is said to be irregular if the degrees of the vertices are distinct. The irregularity strength of a graph is the smallest $s$ such that the edges can be weighted with $\{1,2,3, \cdots, s\}$ and be irregular. This notion was defined by Chartrand et al. (G Chartrand, M. S. Jacobson, J. Lehel, O. R. Ollerman, S. Ruiz \& Saba. 1988). In this paper, we discuss the irregularity strength of corona product of a graph with star graph $K_{1,n}$. We obtain a sufficient condition on the minimum degree of a graph $H$ which determines the irregularity strength of a graph $H$ having $p$ vertices with the star graph $K_{1,n}$.
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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 | 0.007 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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