A class of trees with equal broadcast and domination numbers
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Bibliographic record
Abstract
A broadcast on a graph G is a function f : V →{ 0, 1, 2 ,... }. The broadcast number of G is the minimum value ofv∈V f (v )a mong all broadcasts f for which each vertex of G is within distance f (v )f rom some vertex v with f (v) ≥ 1. The broadcast number is bounded above by the radius and the domination number of G. We consider a class of trees that contains the caterpillars and char- acterize the trees in this class that have equal domination and broad- cast numbers, thus generalizing the results in: (S. M. Seager, Dominating broadcasts of caterpillars, Ars Combin. 88 (2008), 307-319).
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 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