Divisor equitably strong non-split divisor equitable domination in graphs
Bibliographic record
Abstract
In epidemiology, the spread of diseases can be modelled using graphs, where individuals are nodes, and edges represent potential pathways for disease transmission. A non-split dominating set could help identify key individuals (or groups) whose monitoring or immunization would ensure that the rest of the population (the non-dominated group) remains connected and can be controlled in case of disease spread. This approach has the potential to have a significant impact across various areas of medicine. We present the idea of non-split divisor equitable domination in graphs as a way to optimize medical networks. Let Q be a graph with vertex set R(Q) and edge set E (Q). Two vertices h and t are known as degree divisor equitable if gcd(dQ(h), dQ(t)) = 1. F ⊂ R(Q) is known as divisor equitable dominating set of Q if ∀ h ∈ R\F, ∋ a t ∈ F such that h and t are adjacent and degree divisor equitable. The divisor equitable domination number of a graph γde(Q) of Q is the minimum cardinality of a divisor equitable dominating set of Q. In this paper, we introduce the concept of a non-split divisor equitable dominating set, divisor equitably strong non-split divisor equitable dominating set, and divisor equitable independent set and divisor equitable clique number. It also explores the concepts of a divisor equitable vertex dominating set, complement divisor equitable graph, and divisor equitable vertex cut.
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How this classification was reachedexpand
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 | 0.000 |
| 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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".