Some Convex Polytopes Joining Paths and Their Metric Dimension
Bibliographic record
Abstract
In recent years, there is a lot of interest in the topic of conveying the groups of planar graphs with an unvarying metric dimension. A few types of planar graphs have recently had their locating number (or metric dimension) determined, and an outstanding problem concerning these graphs was brought up that: Illustrate the types of planar graphs Υ that can be generated from a graph Φ through the addition of more edges to Φ , such that d i m ( Φ ) = d i m ( Υ ) and V ( Φ ) = V ( Υ ) . While proceeding in a similar directives, we identify two families of radially identical planar graphs with unaltered metric dimension in this study: ϝ n , m and ℷ n , m . We do this by establishing that d i m ( ϝ n , m ) = d i m ( ℷ n , m ) and V ( ϝ n , m ) = V ( ℷ n , m ) , respectively. We acquire another family of a radially symmetrical plane graph (i.e., ℸ n , m ) with a constant metric dimension. We show that all the vertices of these classes of the plane graphs can potentially be identified with just three well-chosen nodes.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 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".