The metric dimension of small distance-regular and strongly regular\n graphs
Bibliographic record
Abstract
A {\\em resolving set} for a graph $\\Gamma$ is a collection of vertices $S$,\nchosen so that for each vertex $v$, the list of distances from $v$ to the\nmembers of $S$ uniquely specifies $v$. The {\\em metric dimension} of $\\Gamma$\nis the smallest size of a resolving set for $\\Gamma$.\n A graph is {\\em distance-regular} if, for any two vertices $u,v$ at each\ndistance $i$, the number of neighbours of $v$ at each possible distance from\n$u$ (i.e. $i-1$, $i$ or $i+1$) depends only on the distance $i$, and not on the\nchoice of vertices $u,v$. The class of distance-regular graphs includes all\ndistance-transitive graphs and all strongly regular graphs.\n In this paper, we present the results of computer calculations which have\nfound the metric dimension of all distance-regular graphs on up to 34 vertices,\nlow-valency distance transitive graphs on up to 100 vertices, strongly regular\ngraphs on up to 45 vertices, rank-$3$ strongly regular graphs on under 100\nvertices, as well as certain other distance-regular graphs.\n
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".